SOLUTION: I need help solving this problem: The side of a square equals the width of a rectangle. The length of the rectangle is 6 meters longer than its width. The sum of the areas of the s

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Question 600757: I need help solving this problem: The side of a square equals the width of a rectangle. The length of the rectangle is 6 meters longer than its width. The sum of the areas of the square and rectangle is 176 square meters. Find the side of the square
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The side of a square equals the width of a rectangle.
The length of the rectangle is 6 meters longer than its width.
The sum of the areas of the square and rectangle is 176 square meters.
Find the side of the square
:
Let x = the side of the square and the width of the rectangle
then
(x+6) = the length of the rectangle
:
Square Area + Rectangle Area = 176 sq/m
x^2 + x(x+6) = 178
x^2 + x^2 + 6x = 176
A quadratic equation
2x^2 + 6x - 176 = 0
This will factor to
(2x + 22)(x - 8) = 0
The positive solution
x = 8 m is the side of the square
;
:
Check this:
8^2 + 8(14) = 176