Identify the dimensions of the rectangle.

Question

Identify the dimensions of the rectangle.

Asked on March 29, 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 · 2026-03-29T13:48:52.844Z

b.i) Step 1: Identify the dimensions of the rectangle. Length ($l$) = $0.003$ m Width ($w$) = $0.0024$ m Step 2: Calculate the perimeter. The formula for the perimeter of a rectangle is $P = 2(l + w)$. $$P = 2(0.003 \text{ m} + 0.0024 \text{ m})$$ $$P = 2(0.0054 \text{ m})$$ $$P = 0.0108 \text{ m}$$ Step 3: Express the perimeter in standard form. Standard form is $a \times 10^n$, where $1 \le |a| < 10$. To move the decimal point two places to the right to get $1.08$, the exponent will be $-2$. $$P = 1.08 \times 10^{-2} \text{ m}$$ The perimeter in standard form is $\boxed{\text{}1.08 \times 10^{-2} \text{ m}}$. b.ii) Step 1: Calculate the area. The formula for the area of a rectangle is $A = l \times w$. $$A = 0.003 \text{ m} \times 0.0024 \text{ m}$$ Step 2: Convert the dimensions to standard form for multiplication. $$0.003 = 3 \times 10^{-3}$$ $$0.0024 = 2.4 \times 10^{-3}$$ Step 3: Multiply the numbers in standard form. $$A = (3 \times 10^{-3}) \times (2.4 \times 10^{-3})$$ $$A = (3 \times 2.4) \times (10^{-3} \times 10^{-3})$$ $$A = 7.2 \times 10^{(-3-3)}$$ $$A = 7.2 \times 10^{-6} \text{ m}^2$$ The area in standard form is $\boxed{\text{}7.2 \times 10^{-6} \text{ m}^2}$.

Accepted Answer · 2026-03-29T13:48:52.844Z

b.i) Step 1: Identify the dimensions of the rectangle. Length ($l$) = $0.003$ m Width ($w$) = $0.0024$ m Step 2: Calculate the perimeter. The formula for the perimeter of a rectangle is $P = 2(l + w)$. $$P = 2(0.003 \text{ m} + 0.0024 \text{ m})$$ $$P = 2(0.0054 \text{ m})$$ $$P = 0.0108 \text{ m}$$ Step 3: Express the perimeter in standard form. Standard form is $a \times 10^n$, where $1 \le |a| < 10$. To move the decimal point two places to the right to get $1.08$, the exponent will be $-2$. $$P = 1.08 \times 10^{-2} \text{ m}$$ The perimeter in standard form is $\boxed{\text{}1.08 \times 10^{-2} \text{ m}}$. b.ii) Step 1: Calculate the area. The formula for the area of a rectangle is $A = l \times w$. $$A = 0.003 \text{ m} \times 0.0024 \text{ m}$$ Step 2: Convert the dimensions to standard form for multiplication. $$0.003 = 3 \times 10^{-3}$$ $$0.0024 = 2.4 \times 10^{-3}$$ Step 3: Multiply the numbers in standard form. $$A = (3 \times 10^{-3}) \times (2.4 \times 10^{-3})$$ $$A = (3 \times 2.4) \times (10^{-3} \times 10^{-3})$$ $$A = 7.2 \times 10^{(-3-3)}$$ $$A = 7.2 \times 10^{-6} \text{ m}^2$$ The area in standard form is $\boxed{\text{}7.2 \times 10^{-6} \text{ m}^2}$.