Question

answer the questions below.
(a) the perimeter of a rectangular field is 330 m.
if the length of the field is 89 m, what is its width?
width of the field: m
(b) the area of a rectangular painting is 5642 cm².
if the width of the painting is 62 cm, what is its length?
length of the painting: cm

Explanation:

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 \(P = 330\) m and \(l = 89\) m. First, substitute into the formula: \(330=2(89 + w)\).

Step2: Solve for \(w\)

Divide both sides of the equation \(330 = 2(89 + w)\) by \(2\): \(\frac{330}{2}=89 + w\), so \(165=89 + w\). Then subtract \(89\) from both sides: \(w=165 - 89\).

Step3: 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 \(A = 5642\) \(cm^{2}\) and \(w = 62\) cm. Substitute into the formula: \(5642=l\times62\).

Step4: Solve for \(l\)

Divide both sides of the equation \(5642=l\times62\) by \(62\): \(l=\frac{5642}{62}\).

Answer:

(a) \(76\) m
(b) \(91\) cm