Question

answer the questions below.
(a) the perimeter of a rectangular garden is 368 m.
if the width of the garden is 85 m, what is its length?
length of the garden:
(b) the area of a rectangular window is 4200 cm².
if the length of the window is 75 cm, what is its width?
width of the window:

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. Given \(P = 368\) m and \(w = 85\) m.

Step2: Solve for the length

First, substitute the values into the formula: \(368=2(l + 85)\).
Divide both sides by 2: \(\frac{368}{2}=l + 85\), so \(184=l + 85\).
Then subtract 85 from both sides: \(l=184 - 85\).
\(l = 99\) 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. Given \(A = 4200\) \(cm^{2}\) and \(l = 75\) cm.

Step2: Solve for the width

Substitute the values into the formula: \(4200 = 75\times w\).
Divide both sides by 75: \(w=\frac{4200}{75}\).
\(w = 56\) cm.

Answer:

(a) \(99\) m
(b) \(56\) cm