Question

answer the questions below. (a) the perimeter of a rectangular field is 296 m. if the width of the field is 64 m, what is its length? length of the field: m (b) the area of a rectangular painting is 3876 cm². if the length of the painting is 76 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 $P = 296$ m and $w=64$ m. First, substitute into the formula: $296 = 2(l + 64)$.

Step2: Solve for length

Divide both sides of the equation by 2: $\frac{296}{2}=l + 64$, so $148=l + 64$. Then subtract 64 from both sides: $l=148 - 64=84$ 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 $A = 3876$ $cm^{2}$ and $l = 76$ cm. Substitute into the formula: $3876=76\times w$.

Step4: Solve for width

Divide both sides of the equation by 76: $w=\frac{3876}{76}=51$ cm.

Answer:

(a) 84
(b) 51