Question

answer the questions below.
(a) the perimeter of a rectangular garden is 258 m.
if the length of the garden is 74 m, what is its width?
width of the garden: ■m
(b) the area of a rectangular window is 6825 cm².
if the width of the window is 75 cm, what is its length?
length of the window: ■cm

Explanation:

(a)

Step1: Recall the perimeter formula for a rectangle

The perimeter formula for a rectangle is \(P = 2(l + w)\), where \(P\) is the perimeter, \(l\) is the length, and \(w\) is the width. We are given \(P = 258\) m and \(l=74\) m.

Step2: Solve for the width

First, substitute the values into the formula: \(258 = 2(74 + w)\).
Divide both sides by 2: \(\frac{258}{2}=74 + w\), so \(129=74 + w\).
Subtract 74 from both sides: \(w = 129 - 74\).
\(w = 55\) m.

(b)

Step1: Recall the area formula for a rectangle

The area formula for a rectangle is \(A=l\times w\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width. We are given \(A = 6825\) \(cm^{2}\) and \(w = 75\) cm.

Step2: Solve for the length

Substitute the values into the formula: \(6825=l\times75\).
Divide both sides by 75: \(l=\frac{6825}{75}\).
\(l = 91\) cm.

Answer:

(a) \(55\) m
(b) \(91\) cm