Question

answer the questions below.
(a) the area of a rectangular field is 7410 m².
if the width of the field is 78 m, what is its length?
length of the field: m
(b) the perimeter of a rectangular painting is 266 cm.
if the length of the painting is 76 cm, what is its width?
width of the painting: cm

Explanation:

Part (a)

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \), so \( \text{length} = \frac{A}{\text{width}} \).

Step2: Substitute values and calculate

Given \( A = 7410 \, \text{m}^2 \) and width \( = 78 \, \text{m} \), then length \( = \frac{7410}{78} = 95 \, \text{m} \).

Part (b)

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is \( P = 2(\text{length} + \text{width}) \), so \( \text{width} = \frac{P}{2} - \text{length} \).

Step2: Substitute values and calculate

Given \( P = 266 \, \text{cm} \) and length \( = 76 \, \text{cm} \), first find \( \frac{P}{2} = \frac{266}{2} = 133 \, \text{cm} \). Then width \( = 133 - 76 = 57 \, \text{cm} \).

Answer:

(a) Length of the field: \( 95 \) m
(b) Width of the painting: \( 57 \) cm