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) (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
; ; .
Can a way be found to put the quadratic area equation completely in terms of x?
, using the w linear equation;
, using the L linear equation;
, again using the w linear equation.
Simplify the quadratic area equation.
, factorable.
From that, .
w=12 and L=14.
Answer by mananth(16946) (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
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