Question

answer the questions below.
(a) the area of a rectangular parking lot is ( 3588 mathrm{~m}^{2} ).
if the width of the parking lot is ( 52 mathrm{~m} ), what is its length?
length of the parking lot: ( square mathrm{m} )
perimeter of a rectangular pool is ( 266 mathrm{~m} ).
if the length of the pool is ( 77 mathrm{~m} ), what is its width?
width of the pool: ( square mathrm{m} )

Explanation:

Part (a)

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 need to solve for \(l\), so \(l=\frac{A}{w}\).

Step2: Substitute the given values

Given \(A = 3588\space m^{2}\) and \(w = 52\space m\). Then \(l=\frac{3588}{52}\).

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Part (b)

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. First, we can simplify the formula to solve for \(w\): \(P = 2l+2w\), then \(2w=P - 2l\), and \(w=\frac{P - 2l}{2}\).

Step2: Substitute the given values

Given \(P = 266\space m\) and \(l = 77\space m\). Then \(w=\frac{266-2\times77}{2}\).

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Answer:

• Length of the parking lot: \(69\space m\)
• Width of the pool: \(56\space m\)