SOLUTION: The combined perimeters of the 2 squares is 52 in. When they are placed together, the third figure is formed. It has an outer perimeter of 42 in. Find the sides.

Question 827182: The combined perimeters of the 2 squares is 52 in. When they are placed together, the third figure is formed. It has an outer perimeter of 42 in. Find the sides.
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
S = side length of smaller
L = side length of larger
4S + 4L = 52
Now consider the figure where the two squares are set next to each other.
This figure will have 3 sides of length L, 3 sides of length S
and additional perimeter where the squares join.
The area where they join can be represented by L - S
So the equation for the new figure is
3L + 3S + L - ( L-S ) = 42 We are subtracting the covered portion.
3L + 3S + L - L + S = 42
3L + 4S = 42
Now we have two equations
4S + 4L = 52
4S + 3L = 42
subtract the bottom from the top
L = 10
Substitute L = 10 in 4S + 3L = 42
4S + 3(10) = 42
4S + 30 = 42
subtract 30 from each side
4S = 12
S = 4
So the smaller square is 4 x 4 and the larger 10 x 10

RELATED QUESTIONS
Four squares are stacked in a tower. The bottom square is 12" on a side. The perimeter of (answered by Herdaysoji)

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 squares of two consecutive even integers is 52. what are the integers? I... (answered by edjones,Earlsdon)

What are the measures of the numbered angles in rhombus PQRS when Q is 104 degrees? The... (answered by fractalier)

An equilateral triangle has a perimeter of 12 cm. By joining the midpoints of its sides... (answered by ikleyn)

1)when a certain rectangle is divided in half, two squares are formed. if each of these... (answered by josgarithmetic)

1)Alan has 5 pairs of trousers and 6 shirts. Ben has 7 pairs of trousers and 4 shirts.... (answered by Edwin McCravy)

The sum of the perimeters of two squares is 40 inches. the sum of their areas is 58... (answered by funmath)

The larger square has an area of 216x^2 and the smaller square has an area of 125x^2.... (answered by Alan3354)