Question

A rectangular swimming pool is 50 meters long and 25 meters wide. A concrete walkway with a width of x meters will surround the pool. The combined area of the pool and the walkway will be 1736 square meters. Solve the equation (50+2x)(25+2x)=1736 to find the width of the walkway. Justify that your answer is reasonable.

Answer 1

Answer: Rectangle ABCD represents the swimming pool.

Rectangle EFGH represents the swimming pool surrounded by the concrete border.

AB = CD = 50 m and BC = DA = 25 m

EF = GH = 50 + 2x3 = 56 m and FG = HF = 25 + 2x3 = 31 m

So, perimeter of outer rectangle i.e. rectangle EFGH = 2(EF + FG) = 2(56 + 31) = 174 m.

Area of the outer rectangle = 56 x 31 = 1736 m%5E2.

Area of the inner rectangle = 50 x 25 = 1250 m%5E2.

So, area of the concrete border = 1736 - 1250 = 486 m%5E2.

Step-by-step explanation: Image shown.