Question

answer the questions below. (a) the perimeter of a rectangular garden is 284 m. if the length of the garden is 78 m, what is its width? width of the garden: □ m (b) the area of a rectangular window is 7252 cm². if the width of the window is 74 cm, what is its length? length of the window: □ cm

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$, where $P$ is the perimeter, $l$ is the length and $w$ is the width. Given $P = 284$ m and $l=78$ m.

Step2: Substitute values into formula

$284 = 2(78 + w)$
First, divide both sides by 2: $\frac{284}{2}=78 + w$, so $142=78 + w$.

Step3: Solve for width

Subtract 78 from both sides: $w=142 - 78=64$ m.

Step4: 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 $A = 7252$ $cm^{2}$ and $w = 74$ cm.

Step5: Substitute values into formula

$7252=l\times74$.

Step6: Solve for length

Divide both sides by 74: $l=\frac{7252}{74}=98$ cm.

Answer:

Width of the garden: 64 m
Length of the window: 98 cm