Question

answer the questions below. (a) the perimeter of a rectangular field is 324 m. if the width of the field is 68 m, what is its length? length of the field: m (b) the area of a rectangular painting is 5330 cm². if the length of the painting is 82 cm, what is its width? width of the painting: cm

Explanation:

Step1: 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. Given $P=324$ m and $w = 68$ m. We can rewrite the formula to solve for $l$: $l=\frac{P}{2}-w$.

Step2: Calculate length for part (a)

Substitute $P = 324$ and $w = 68$ into the formula: $l=\frac{324}{2}-68=162 - 68=94$ m.

Step3: 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. Given $A = 5330$ cm² and $l = 82$ cm. We can rewrite the formula to solve for $w$: $w=\frac{A}{l}$.

Step4: Calculate width for part (b)

Substitute $A = 5330$ and $l = 82$ into the formula: $w=\frac{5330}{82}=65$ cm.

Answer:

(a) 94 m
(b) 65 cm