Question

answer the questions below.
(a) the perimeter of a rectangular garden is 338 m.
if the width of the garden is 74 m, what is its length?
length of the garden: m
(b) the area of a rectangular window is 8316 cm².
if the length of the window is 99 cm, what is its width?
width of the window: cm

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times (length + width) \). We know \( P = 338 \) m and \( width = 74 \) m. Let \( l \) be the length. So, \( 338 = 2\times (l + 74) \).

Step2: Solve for length

First, divide both sides by 2: \( \frac{338}{2}=l + 74 \), which simplifies to \( 169 = l + 74 \). Then, subtract 74 from both sides: \( l = 169 - 74 = 95 \) m.

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is \( A = length\times width \). We know \( A = 8316 \) \( cm^2 \) and \( length = 99 \) cm. Let \( w \) be the width. So, \( 8316 = 99\times w \).

Step2: Solve for width

Divide both sides by 99: \( w=\frac{8316}{99}=84 \) cm.

Answer:

(a) Length of the garden: \( 95 \) m
(b) Width of the window: \( 84 \) cm