Question

(a) the area of a rectangular garden is 4071 m². if the width of the garden is 59 m, what is its length? length of the garden: m (b) the perimeter of a rectangular window is 372 cm. if the length of the window is 99 cm, what is its width? width of the window: cm

Explanation:

Step1: Find the length of the garden

The area formula of a rectangle is \(A = l\times w\) (where \(A\) is area, \(l\) is length, \(w\) is width). Given \(A = 4071m^{2}\) and \(w = 59m\).
We can find \(l\) by \(l=\frac{A}{w}\).
Substitute the values: \(l=\frac{4071}{59}\).
\(4071\div59 = 69\)

Step2: Find the width of the window

The perimeter formula of a rectangle is \(P=2(l + w)\) (where \(P\) is perimeter, \(l\) is length, \(w\) is width). Given \(P = 372cm\) and \(l = 99cm\).
First, rewrite the formula for \(w\): \(w=\frac{P}{2}-l\).
Substitute \(P = 372\) and \(l = 99\): \(w=\frac{372}{2}-99\).
\(\frac{372}{2}=186\), then \(186 - 99=87\)

Answer:

(a) Length of the garden: \(69m\)
(b) Width of the window: \(87cm\)