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.

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.

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times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3