SOLUTION: The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 96 squ

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Question 597485: The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 96 square centimeters. Find the side of the square.
Answer by lwsshak3(11628) About Me  (Show Source):
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The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 96 square centimeters. Find the side of the square.
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I will assume you meant the width of the rectangle is 4 cm instead of 4 m longer than the length.
..
let x=side of square
length of rectangle=x
width of rectangle =x+4
area of square=x^2
area of rectangle=length*width=x(x+4)
area of square+area of rectangle=96
x^2+x(x+4)=96
x^2+x^2+4x=96
2x^2+4x-96=0
x^2+2x-48=0
(x+8)(x-6)=0
x=-8 (reject, x>0)
x=6
ans:
side of square=6 cm