SOLUTION: 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?

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?
:
Let the sides of one square be: x
Let the sides of the other square be:y
:
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:
:
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!!!

RELATED QUESTIONS
Okay here goes nothing.. The sum of the perimeters of two squares is 40 inches. The... (answered by faceoff57,funmath)

the sum of the perimeters of two square lots is 140 meters while the sum of their areas... (answered by ankor@dixie-net.com)

The sides of the outside square are 6 inches long. The corners of the next smaller... (answered by jhardin)

If the area between 2 squares is 17 inches and the sum of the perimeters of the 2 squares (answered by macston)

Two squares have perimeters of 20 inches and 48 inches. How much longer is a side of the... (answered by MathLover1)

The perimeters of two squares are in a ratio of 4 to 9. What is the ratio between the... (answered by josmiceli)

the sum of the areas of two squares is 234 square inches. Each side of the larger square... (answered by mananth)

The figure below consists of a smaller square inside a larger one. The difference in... (answered by ikleyn)

The sum of the perimeter of two squares is 64cm. and the sum of their areas is 130sq.cm.... (answered by ankor@dixie-net.com)