SOLUTION: The figure below consists of a smaller square inside a larger one. The difference in their areas (the shaded part) is 17 cm². The sum of the perimeters of the two squares is 68 cm

Question 1157422: The figure below consists of a smaller square inside a larger one. The difference in their areas (the shaded part) is 17 cm². The sum of the perimeters of the two squares is 68 cm. How long are the sides of the larger square?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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From the condition, you have 2 equations


    x + y     = 17.        (1)

    x^2 - y^2 = 17.        (2)


Factor equation (2)

    (x+y)*(x-y) = 17.


Replace here x+y by 17, based on equation (1).  You will get

    17*(x-y) = 17,   or  x-y = 1.


Thus, instead of equations (1) and (2), you have much simpler system

    x + y = 17    (3)

    x - y =  1    (4)


Add the equations, and get 2x - 19,  x = 9.


Hence,  y = 17-9 = 8.


ANSWER.  The sides of the square are 9 cm  and  8 cm.

Solved.

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