Question

answer the questions below.
(a) the area of a rectangular field is 6674 m².
if the width of the field is 71 m, what is its length?
length of the field: m
(b) the perimeter of a rectangular painting is 238 cm.
if the length of the painting is 68 cm, what is its width?
width of the painting: cm

Explanation:

(a)

Step1: Recall the area formula for a rectangle

The area formula for a rectangle is \(A = l\times w\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width. We need to solve for \(l\), so \(l=\frac{A}{w}\).

Step2: Substitute the given values

Given \(A = 6674\space m^{2}\) and \(w = 71\space m\). Then \(l=\frac{6674}{71}\).

$$l=\frac{6674}{71}=94\space m$$

(b)

Step1: Recall the perimeter formula for a rectangle

The perimeter formula for a rectangle is \(P=2(l + w)\), where \(P\) is the perimeter, \(l\) is the length, and \(w\) is the width. First, solve the formula for \(w\):

$$P = 2(l + w)$$

$$ \frac{P}{2}=l + w$$

$$w=\frac{P}{2}-l$$

Step2: Substitute the given values

Given \(P = 238\space cm\) and \(l = 68\space cm\). Then \(w=\frac{238}{2}-68\).

$$w = 119-68=51\space cm$$

Answer:

(a) \(94\space m\)
(b) \(51\space cm\)