Question

answer the questions below. (a) the area of a rectangular field is 5141 m². if the width of the field is 53 m, what is its length? length of the field: m (b) the perimeter of a rectangular painting is 370 cm. if the length of the painting is 98 cm, what is its width? width of the painting: cm

Explanation:

Step1: Recall area formula

The area formula of a rectangle is $A = l\times w$, where $A$ is area, $l$ is length and $w$ is width. We need to find $l$, so $l=\frac{A}{w}$.

Step2: Calculate length for part (a)

Given $A = 5141\ m^{2}$ and $w = 53\ m$, then $l=\frac{5141}{53}=97\ m$.

Step3: Recall perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$, where $P$ is perimeter, $l$ is length and $w$ is width. We can rewrite it to find $w$: $w=\frac{P}{2}-l$.

Step4: Calculate width for part (b)

Given $P = 370\ cm$ and $l = 98\ cm$. First, $\frac{P}{2}=\frac{370}{2}=185\ cm$. Then $w=185 - 98=87\ cm$.

Answer:

(a) 97 m
(b) 87 cm