SOLUTION: The combined area of a square and a rectangle is 76 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of

Algebra ->  Rectangles -> SOLUTION: The combined area of a square and a rectangle is 76 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of       Log On


   

Question 585359: The combined area of a square and a rectangle is 76 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 4 centimeters more than its width. Find the dimensions of the square and the rectangle.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The combined area of a square and a rectangle is 76 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 4 centimeters more than its width.
Find the dimensions of the square and the rectangle.
:
Let x = the side of the square
then the rectangle dimensions:
W = (x+2)
length is 4 cm more than the width:
L = (x + 2 + 4)
L = (x+6)
:
Area of both:
x^2 + (x+2)(x+6) = 76
FOIL
x^2 + x^2 + 6x + 2x + 12 - 76 = 0
Combine like terms
2x^2 + 8x - 64 = 0
Simplify, divide by 2
x^2 + 4x - 32 = 0
Factors to
(x+8)(x-4) = 0
The positive solution is all we want here
x = 4 cm is the side of the square
:
I'll let you find the dimensions of the rectangle, check it by finding the total area