a. Draw a pie chart to illustrate the information b. Find the percentage of the total expenditure allocated to education. c. The area of a rectangle is 63cm² and its length is 9cm, find its width.

Question

Asked on August 24, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-08-24T20:34:38.672Z

Here are the solutions to the questions: Question Two (2) a) To construct triangle PQR and its incircle: Step 1: Draw a line segment PQ of length 9 cm. Step 2: At point Q, use a protractor or compass and ruler to construct an angle of 75^ ( PQR). Step 3: At point P, construct an angle of 60^ ( QPR). Step 4: Extend the rays from P and Q until they intersect at point R, forming PQR. Step 5: To locate point T (the incenter), bisect any two angles of the triangle (e.g., P and Q). The intersection of these two angle bisectors is point T. Step 6: From point T, draw a perpendicular line segment to any side of the triangle (e.g., PQ). Let the point where it touches PQ be S. The length of TS is the radius of the incircle. Step 7: With T as the center and TS as the radius, draw a circle. This circle will touch all three sides of PQR. (Note: I cannot physically measure the radius for you.) b) Using the given triangle: The side opposite to is 5. The side adjacent to is 12. The hypotenuse is 13. i) : Step 1: Recall the definition of sine. = OppositeHypotenuse Step 2: Substitute the values. = (5)/(13) ii) : Step 1: Recall the definition of cosine. = AdjacentHypotenuse Step 2: Substitute the values. = (12)/(13) iii) : Step 1: Recall the definition of tangent. = OppositeAdjacent Step 2: Substitute the values. = (5)/(12) The trigonometric ratios are: i) (5)/(13), ii) (12)/(13), iii) (5)/(12). c) To find the area of a circle: Step 1: Determine the radius from the given diameter. Diameter = 18 cm Radius (r) = Diameter2 = 18 cm2 = 9 cm Step 2: Use the formula for the area of a circle. Area (A) = r^2 Step 3: Substitute the radius and calculate. A = (9 cm)^2 = 81 cm^2 A ≈ 81 × 3.14159 cm^2 ≈ 254.469 cm^2 Step 4: Round to two decimal places. A ≈ 254.47 cm^2 The area of the circle is 254.47 cm^2. Question Three (3) a) To draw a pie chart, we first need to calculate the total expenditure and the angle for each sector. Step 1: Calculate the total expenditure. Total Expenditure = 84 + 90 + 54 + 72 + 54 + 78 = 432 (thousand cedis) Step 2: Calculate the angle for each service. • Health: (84)/(432) × 360^ = 70^ • Primary Education: (90)/(432) × 360^ = 75^ • Secondary Education: (54)/(432) × 360^ = 45^ • Transport: (72)/(432) × 360^ = 60^ • Police: (54)/(432) × 360^ = 45^ • Housing: (78)/(432) × 360^ = 65^ (Note: To draw the pie chart, you would draw a circle, mark the center, and then use a protractor to draw sectors with these calculated angles.) b) To find the percentage of total expenditure allocated to education: Step 1: Calculate the total expenditure on education. Education Expenditure = Primary Education + Secondary Education = 90 + 54 = 144 (thousand cedis) Step 2: Calculate the percentage of total expenditure. Percentage = Education ExpenditureTotal Expenditure × 100\% Percentage = (144)/(432) × 100\% Percentage = (1)/(3) × 100\% ≈ 33.33\% The percentage of total expenditure allocated to education is 33.33\%. c) To find the width of a rectangle: Step 1: Recall the formula for the area of a rectangle. Area = Length × Width Step 2: Substitute the given values. 63 cm^2 = 9 cm × Width Step 3: Solve for the width. Width = 63 cm^29 cm = 7 cm The width of the rectangle is 7 cm. Send me the next one 📸

Accepted Answer · 2026-08-24T20:34:38.672Z

Here are the solutions to the questions: Question Two (2) a) To construct triangle PQR and its incircle: Step 1: Draw a line segment PQ of length 9 cm. Step 2: At point Q, use a protractor or compass and ruler to construct an angle of 75^ ( PQR). Step 3: At point P, construct an angle of 60^ ( QPR). Step 4: Extend the rays from P and Q until they intersect at point R, forming PQR. Step 5: To locate point T (the incenter), bisect any two angles of the triangle (e.g., P and Q). The intersection of these two angle bisectors is point T. Step 6: From point T, draw a perpendicular line segment to any side of the triangle (e.g., PQ). Let the point where it touches PQ be S. The length of TS is the radius of the incircle. Step 7: With T as the center and TS as the radius, draw a circle. This circle will touch all three sides of PQR. (Note: I cannot physically measure the radius for you.) b) Using the given triangle: The side opposite to is 5. The side adjacent to is 12. The hypotenuse is 13. i) : Step 1: Recall the definition of sine. = OppositeHypotenuse Step 2: Substitute the values. = (5)/(13) ii) : Step 1: Recall the definition of cosine. = AdjacentHypotenuse Step 2: Substitute the values. = (12)/(13) iii) : Step 1: Recall the definition of tangent. = OppositeAdjacent Step 2: Substitute the values. = (5)/(12) The trigonometric ratios are: i) (5)/(13), ii) (12)/(13), iii) (5)/(12). c) To find the area of a circle: Step 1: Determine the radius from the given diameter. Diameter = 18 cm Radius (r) = Diameter2 = 18 cm2 = 9 cm Step 2: Use the formula for the area of a circle. Area (A) = r^2 Step 3: Substitute the radius and calculate. A = (9 cm)^2 = 81 cm^2 A ≈ 81 × 3.14159 cm^2 ≈ 254.469 cm^2 Step 4: Round to two decimal places. A ≈ 254.47 cm^2 The area of the circle is 254.47 cm^2. Question Three (3) a) To draw a pie chart, we first need to calculate the total expenditure and the angle for each sector. Step 1: Calculate the total expenditure. Total Expenditure = 84 + 90 + 54 + 72 + 54 + 78 = 432 (thousand cedis) Step 2: Calculate the angle for each service. • Health: (84)/(432) × 360^ = 70^ • Primary Education: (90)/(432) × 360^ = 75^ • Secondary Education: (54)/(432) × 360^ = 45^ • Transport: (72)/(432) × 360^ = 60^ • Police: (54)/(432) × 360^ = 45^ • Housing: (78)/(432) × 360^ = 65^ (Note: To draw the pie chart, you would draw a circle, mark the center, and then use a protractor to draw sectors with these calculated angles.) b) To find the percentage of total expenditure allocated to education: Step 1: Calculate the total expenditure on education. Education Expenditure = Primary Education + Secondary Education = 90 + 54 = 144 (thousand cedis) Step 2: Calculate the percentage of total expenditure. Percentage = Education ExpenditureTotal Expenditure × 100\% Percentage = (144)/(432) × 100\% Percentage = (1)/(3) × 100\% ≈ 33.33\% The percentage of total expenditure allocated to education is 33.33\%. c) To find the width of a rectangle: Step 1: Recall the formula for the area of a rectangle. Area = Length × Width Step 2: Substitute the given values. 63 cm^2 = 9 cm × Width Step 3: Solve for the width. Width = 63 cm^29 cm = 7 cm The width of the rectangle is 7 cm. Send me the next one 📸

a. Draw a pie chart to illustrate the information b. Find the percentage of the total expenditure allocated to education. c. The area of a rectangle is 63cm² and its length is 9cm, find its width.

Need help with your own homework?

More Mathematics Questions

a. Draw a pie chart to illustrate the information b. Find the percentage of the total expenditure allocated to education. c. The area of a rectangle is 63cm² and its length is 9cm, find its width.

Need help with your own homework?

More Mathematics Questions