Question

answer the questions below.
(a) the area of a rectangular garden is 7742 m².
if the width of the garden is 79 m, what is its length?
length of the garden: m
(b) the perimeter of a rectangular window is 292 cm.
if the length of the window is 87 cm, what is its width?
width of the window: cm

Explanation:

Step1: Recall the formula for the area of a 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. We need to find \(l\), so we can rewrite the formula as \(l=\frac{A}{w}\). Given \(A = 7742\space m^{2}\) and \(w = 79\space m\).

Step2: Calculate the length of the garden

Substitute the values into the formula: \(l=\frac{7742}{79}\). Using long - division or a calculator, \(7742\div79 = 98\).

Step3: Recall the formula for the perimeter of a 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. We can rewrite it to solve for \(w\): \(w=\frac{P}{2}-l\). Given \(P = 292\space cm\) and \(l = 87\space cm\).

Step4: Calculate the width of the window

First, find \(\frac{P}{2}\): \(\frac{292}{2}=146\). Then subtract the length: \(w = 146-87\). \(146 - 87=59\).

Answer:

(a) \(98\) m
(b) \(59\) cm