Question

answer the questions below.
(a) the perimeter of a rectangular garden is 294 m.
if the length of the garden is 82 m, what is its width?
width of the garden:
(b) the area of a rectangular window is 5568 cm².
if the width of the window is 64 cm, what is its length?
length of the window:

Explanation:

(a)

Step1: Recall the perimeter formula for 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. Given \(P=294\) m and \(l = 82\) m.

Step2: Substitute the values into the formula and solve for \(w\)

We have \(294=2(82 + w)\). First, divide both sides by 2: \(\frac{294}{2}=82 + w\), so \(147=82 + w\). Then subtract 82 from both sides: \(w=147 - 82\).

(b)

Step1: Recall the area formula for 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. Given \(A = 5568\) \(cm^{2}\) and \(w = 64\) cm.

Step2: Substitute the values into the formula and solve for \(l\)

We have \(5568=l\times64\). Then \(l=\frac{5568}{64}\).

Answer:

(a) \(w = 65\) m
(b) \(l = 87\) cm