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.
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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.
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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