Question

answer the questions below.
(a) the area of a rectangular field is 5576 m².
if the length of the field is 82 m, what is its width?
width of the field: m
(b) the perimeter of a rectangular painting is 246 cm.
if the width of the painting is 52 cm, what is its length?
length of the painting: cm

Explanation:

Step1: Recall the formula for the area of 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. We need to solve for \(w\), so \(w=\frac{A}{l}\). Given \(A = 5576\space m^{2}\) and \(l = 82\space m\), then \(w=\frac{5576}{82}\).

Step2: Calculate the width

\(\frac{5576}{82}=68\space m\)

Step3: Recall the formula for the perimeter of 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. We can rewrite it to solve for \(l\): \(l=\frac{P}{2}-w\). Given \(P = 246\space cm\) and \(w = 52\space cm\), then \(l=\frac{246}{2}-52\).

Step4: Calculate the length

First, \(\frac{246}{2}=123\). Then \(123 - 52=71\space cm\)

Answer:

(a) \(68\space m\)
(b) \(71\space cm\)