Question

the area of a rectangular field is 6612 m². if the length of the field is 87 m, what is its width? width of the field: m
the perimeter of a rectangular painting is 280 cm. if the width of the painting is 63 cm, what is its length? length of the painting: cm

Explanation:

Step1: Recall area formula for rectangle

The area formula of a rectangle is $A = l\times w$, where $A$ is the area, $l$ is the length and $w$ is the width. Given $A = 6612$ m² and $l = 87$ m. We can find $w$ by rearranging the formula to $w=\frac{A}{l}$.
$w=\frac{6612}{87}$

Step2: Calculate the width

$w = 76$ m

Step3: Recall perimeter formula for rectangle

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 280$ cm and $w = 63$ cm. We can find $l$ by first expanding the formula: $P = 2l+2w$, then rearranging to solve for $l$: $2l=P - 2w$, and $l=\frac{P - 2w}{2}$.
$l=\frac{280-2\times63}{2}$

Step4: Calculate the length

First, calculate $2\times63 = 126$. Then $280-126 = 154$. Finally, $\frac{154}{2}=77$ cm

Answer:

(a) 76 m
(b) 77 cm