Question

a rectangular swimming pool is 25 meters long and 10 meters wide. a walkway is being built around the pool, and the width of the walkway is 2 meters. which number sentence shows the total length of fencing needed to enclose both the pool and the walkway in meters?
○ (25 + 2) × (10 + 2) = 324 square meters
○ (25 + 2 + 2) × (10 + 2 + 2) = 406 square meters
○ 2(25 + 2) + 2(10 + 2) = 78 meters
○ 2(25 + 2 + 2) + 2(10 + 2 + 2) = 86 meters

Explanation:

Step1: Calculate the new length and width

Since the walkway is 2 meters wide on both sides, the new length is \(25 + 2+2\) meters and the new width is \(10 + 2 + 2\) meters.

Step2: Use the perimeter formula for a rectangle

The perimeter formula of a rectangle is \(P=2l + 2w\) (where \(l\) is length and \(w\) is width). Substitute \(l = 25+2 + 2\) and \(w=10 + 2+2\) into the formula, we get \(P = 2(25+2 + 2)+2(10 + 2+2)\).

Answer:

\(2(25 + 2+2)+2(10 + 2+2)=86\) meters (the fourth option)