Find the area of a square whose perimeter is 32cm.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the questions:

1. Find the area of a square whose perimeter is 32cm.

Find the side length of the square.
The perimeter of a square is given by $P = 4s$ , where $s$ is the side length.
$32 \text{ cm} = 4s$ $s = \frac{32}{4} \text{ cm}$ $s = 8 \text{ cm}$
Calculate the area of the square.
The area of a square is given by $A = s^2$ .
$A = (8 \text{ cm})^2$ $A = 64 \text{ cm}^2$
The correct option is C.
$\boxed{\text{C. } 64 \text{ cm}^2}$
2. If $39 + 4 \times B = 55$ . What is B?
Subtract 39 from both sides of the equation.
$39 + 4B = 55$ $4B = 55 - 39$ $4B = 16$
Divide by 4 to find B.
$B = \frac{16}{4}$ $B = 4$
The correct option is C.
$\boxed{\text{C. } 4}$
3. Convert 0.375 into fraction.
Write the decimal as a fraction over a power of 10.
$0.375 = \frac{375}{1000}$
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor.
Divide by 25:
$\frac{375 \div 25}{1000 \div 25} = \frac{15}{40}$
Divide by 5:
$\frac{15 \div 5}{40 \div 5} = \frac{3}{8}$
The correct option is D.
$\boxed{\text{D. } \frac{3}{8}}$
4. Find the value of $7^3$ .
Calculate $7^3$ .
$7^3 = 7 \times 7 \times 7$ $7^3 = 49 \times 7$ $7^3 = 343$
The correct option is D.
$\boxed{\text{D. } 343}$
5. Simplify: $(36 - 12) \div (6 - 3)$
Perform the operations inside the parentheses.
$(36 - 12) = 24$ $(6 - 3) = 3$
Perform the division.
$24 \div 3 = 8$
The correct option is D.
$\boxed{\text{D. } 8}$
6. Express 615 in Roman Numerals.
Break down the number into Roman numeral components.
600 is DC (D = 500, C = 100, so DC = 500 + 100 = 600)
10 is X
5 is V
Combine the components.
$615 = 600 + 10 + 5 = \text{DCXV}$
The correct option is C.
$\boxed{\text{C. DCXV}}$
7. Write in words: 605005.
Identify the place values of the digits.
6 is in the hundred thousands place.
0 is in the ten thousands place.
5 is in the thousands place.
0 is in the hundreds place.
0 is in the tens place.
5 is in the ones place.
Write the number in words based on its place values.
The number is "Six hundred five thousand and five".
The correct option is D.
$\boxed{\text{D. Six hundred five thousand and five}}$
8. Mr. Ugochukwu earns N10,000.00 a month and saves N2000. What percentage of his salary does he save?
Identify the amount saved and the total salary.
Amount saved = N2000
Total salary = N10,000
Calculate the percentage saved.
$\text{Percentage saved} = \left(\frac{\text{Amount saved}}{\text{Total salary}}\right) \times 100\%$ $\text{Percentage saved} = \left(\frac{2000}{10000}\right) \times 100\%$ $\text{Percentage saved} = \frac{1}{5} \times 100\%$ $\text{Percentage saved} = 20\%$
The correct option is B.
$\boxed{\text{B. } 20\%}$
9. 7 erasers cost N98.00, find the cost of 10 erasers.
Find the cost of one eraser.
$\text{Cost of 1 eraser} = \frac{\text{Total cost}}{\text{Number of erasers}}$ $\text{Cost of 1 eraser} = \frac{\text{N}98.00}{7}$ $\text{Cost of 1 eraser} = \text{N}14.00$
Calculate the cost of 10 erasers.
$\text{Cost of 10 erasers} = 10 \times \text{N}14.00$ $\text{Cost of 10 erasers} = \text{N}140.00$
The correct option is C.
$\boxed{\text{C. N}140.00}$
10. Express 32:12 as a ratio in its simplest form.
Write the ratio.
$32:12$
Find the greatest common divisor (GCD) of 32 and 12.
The factors of 32 are 1, 2, 4, 8, 16, 32.
The factors of 12 are 1, 2, 3, 4, 6, 12.
The GCD is 4.
Divide both parts of the ratio by the GCD.
$\frac{32}{4} : \frac{12}{4}$ $8:3$
The correct option is B.
$\boxed{\text{B. } 8:3}$
11. A girl walked 7km in 2hrs and 5km in 1hr. What was her average speed?
Calculate the total distance walked.
$\text{Total distance} = 7 \text{ km} + 5 \text{ km} = 12 \text{ km}$
Calculate the total time taken.
$\text{Total time} = 2 \text{ hrs} + 1 \text{ hr} = 3 \text{ hrs}$
Calculate the average speed.
$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$ $\text{Average speed} = \frac{12 \text{ km}}{3 \text{ hrs}}$ $\text{Average speed} = 4 \text{ km/hr}$
The correct option is C.
$\boxed{\text{C. } 4 \text{ km/hr}}$
12. Write in figure: Fifty thousand and seventy nine.
Break down the number into its components.
Fifty thousand = 50,000
Seventy nine = 79
Add the components.
$50,000 + 79 = 50079$
The correct option is C.
$\boxed{\text{C. } 50079}$
13. Calculate the average of the following set of numbers: 5, 16, 18, 15 and 11.
Sum the numbers in the set.
$\text{Sum} = 5 + 16 + 18 + 15 + 11$ $\text{Sum} = 65$
Count the number of values in the set.
There are 5 numbers.
Calculate the average.
$\text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}}$ $\text{Average} = \frac{65}{5}$ $\text{Average} = 13$
The correct option is A.
$\boxed{\text{A. } 13}$
14. What fraction of 2 minutes is 6 seconds?
Convert 2 minutes to seconds.
$2 \text{ minutes} = 2 \times 60 \text{ seconds} = 120 \text{ seconds}$
Form the fraction.
$\text{Fraction} = \frac{6 \text{ seconds}}{120 \text{ seconds}}$
Simplify the fraction.
$\text{Fraction} = \frac{6}{120}$ $\text{Fraction} = \frac{1}{20}$ $\boxed{\frac{1}{20}}$
15. A book costing N150 was sold for N180.00. Find the percentage profit.
Calculate the profit.
$\text{Profit} = \text{Selling Price} - \text{Cost Price}$ $\text{Profit} = \text{N}180 - \text{N}150$ $\text{Profit} = \text{N}30$
Calculate the percentage profit.
$\text{Percentage Profit} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100\%$ $\text{Percentage Profit} = \left(\frac{30}{150}\right) \times 100\%$ $\text{Percentage Profit} = \frac{1}{5} \times 100\%$ $\text{Percentage Profit} = 20\%$
The correct option is A.
$\boxed{\text{A. } 20\%}$
16. Ade picked 1590 shells, Yemi picked 495 more than Ade. How many shells did Yemi pick?
Add the extra shells Yemi picked to Ade's total.
$\text{Yemi's shells} = \text{Ade's shells} + 495$ $\text{Yemi's shells} = 1590 + 495$ $\text{Yemi's shells} = 2085$
The correct option is B.
$\boxed{\text{B. } 2085}$
17. Divide 1.25 by 0.25.
Write the division as a fraction.
$\frac{1.25}{0.25}$
Multiply the numerator and denominator by 100 to remove the decimals.
$\frac{1.25 \times 100}{0.25 \times 100} = \frac{125}{25}$
Perform the division.
$\frac{125}{25} = 5$
The correct option is C.
$\boxed{\text{C. } 5}$
18. The weekly allowance of a labourer is N1,425.00. If the paymaster paid out N12,825.00 at the end of the week. How many labourers did he pay?
Divide the total amount paid by the allowance per labourer.
$\text{Number of labourers} = \frac{\text{Total amount paid}}{\text{Allowance per labourer}}$ $\text{Number of labourers} = \frac{\text{N}12825.00}{\text{N}1425.00}$
Perform the division.
$\text{Number of labourers} = 9$
The correct option is A.
$\boxed{\text{A. } 9}$

Find the area of a square whose perimeter is 32cm.

Answer

Step-by-step solution

Find the side length of the square.

Calculate the area of the square.

Subtract 39 from both sides of the equation.

Divide by 4 to find B.

Write the decimal as a fraction over a power of 10.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Calculate 737^373.

Perform the operations inside the parentheses.

Perform the division.

Break down the number into Roman numeral components.

Combine the components.

Identify the place values of the digits.

Write the number in words based on its place values.

Identify the amount saved and the total salary.

Calculate the percentage saved.

Find the cost of one eraser.

Calculate the cost of 10 erasers.

Write the ratio.

Find the greatest common divisor (GCD) of 32 and 12.

Divide both parts of the ratio by the GCD.

Calculate the total distance walked.

Calculate the total time taken.

Calculate the average speed.

Break down the number into its components.

Add the components.

Sum the numbers in the set.

Count the number of values in the set.

Calculate the average.

Convert 2 minutes to seconds.

Form the fraction.

Simplify the fraction.

Calculate the profit.

Calculate the percentage profit.

Add the extra shells Yemi picked to Ade's total.

Write the division as a fraction.

Multiply the numerator and denominator by 100 to remove the decimals.

Perform the division.

Divide the total amount paid by the allowance per labourer.

Perform the division.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Calculate $7^3$ .