Question

answer the questions below.
(a) the perimeter of a rectangular garden is 342 m.
if the width of the garden is 75 m, what is its length?
length of the garden: m
(b) the area of a rectangular window is 6351 cm².
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 perimeter of a rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Given \(P=342\) m and \(w = 75\) m. First, substitute into the formula: \(342=2(l + 75)\).

Step2: Solve for \(l\)

Divide both sides of the equation \(342 = 2(l + 75)\) by 2: \(\frac{342}{2}=l + 75\), so \(171=l + 75\). Then subtract 75 from both sides: \(l=171 - 75\).

Step3: Recall the formula for the area of a rectangle

The formula for the area \(A\) of a rectangle is \(A=l\times w\), where \(l\) is the length and \(w\) is the width. Given \(A = 6351\) \(cm^{2}\) and \(l = 87\) cm. Substitute into the formula: \(6351=87\times w\).

Step4: Solve for \(w\)

Divide both sides of the equation \(6351 = 87\times w\) by 87: \(w=\frac{6351}{87}\).

Answer:

(a) \(l=171 - 75=96\) m.
(b) \(w=\frac{6351}{87}=73\) cm.