Question 59609: The sum of the perimeters of two squares is 40 inches. the sum of their areas is 58 square inches. What are the dimensions of the squares? Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website! The sum of the perimeters of two squares is 40 inches. the sum of their areas is 58 square inches. What are the dimensions of the squares?
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Let the sides of one square be: x
Let the sides of the other square be:y
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The perimeter of a square is: , p=perimeter, s=side
E1) Therefore the sum of the perimeters is 40 is:
:
The area of a square is: , A=area, s=side
E2) Therefore the sunm of their area is 58 is:
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Therefore you have two equations and two unknowns. Solve E1 for either variable, I'm going with y.
4x+4y=40
-4x+4x+4y=-4x+40
4y=-4x+40
y=-x+10
Substitute that into E2 for y and solve for x: Factor
(x-3)(x-7)=0 set each parentheses = to 0
x-3=0 and x-7=0
x-3+3=0+3 and x-7+7=0+7
x=3 and x=7
If you were to substitute either x into E1 you'd get the other x
4(3)+4y=40
12+4y=40
4y=28
4y/4=28/4
y=7 You can check 7 for yourself, you'll get 3.
One square is 3 in x 3 in
the other is 7 in x 7 in
Happy Calculating!!!
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