SOLUTION: The combined area of a square and a rectangle is 268 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of

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Question 901563: The combined area of a square and a rectangle is 268 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of the rectangle is 2 centimeters more than its width. Find the dimensions of the square and the rectangle.
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x side of the square
w width of the rectangle
L length of the rectangle

x%5E2%2BwL=268; w=2%2Bx; L=2%2Bw.

Can a way be found to put the quadratic area equation completely in terms of x?

x%5E2%2B%28x%2B2%29L=268, using the w linear equation;
x%5E2%2B%28x%2B2%29%28w%2B2%29=268, using the L linear equation;
x%5E2%2B%28x%2B2%29%282%2Bx%2B2%29=268, again using the w linear equation.

Simplify the quadratic area equation.
x%5E2%2B%28x%2B2%29%28x%2B4%29-268=0
x%5E2%2Bx%5E2%2B6x%2B8-268=0
2x%5E2%2B6x-260=0
x%5E2%2B3x-130=0, factorable.
highlight_green%28%28x-10%29%28x%2B13%29=0%29

From that, highlight%28x=10%29.
w=12 and L=14.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
length of square = x
area = x^2
width of rectangle = x+2
length of rectangle = x+4
Area = (x+2)(x+4)
x^2+6x+8
sum of areas = x^2+x^2+6x+8
2x^2+6x+8 =268
2x^2+6x-260=0
/2
x^2+3x-130=0
x^2+13x-10x-130=0
x(x+13)-10(x+13)=0
(x+13)(x-10)-0
x= 10 taking positive value
side of square =10 cm