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The area of square $ABCD$ is 36 square inches. The area of rectangle $WXYZ$ is 24 square inches. If the two shapes have equal perimeters, what is the length of the longer side of rectangle $WXYZ$?

 Oct 12, 2023
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Side of square =  6

Perimeter =  24

 

Area of rectangle =  x *  y  =  24

Perimeter of rectangle     2 ( x + y)  =  24

So     x + y   = 12

So        y  =  12 - x

 

So

 

x ( 12 -x)  =  24

-x^2 + 12x  =24

x^2 - 12x + 24  =  0     complete the square on x

 

x^2 -12x + 36  =  -24 + 36

(x -6)^2  =  12         take the positive root

x - 6  =  sqrt (12)

x = 6 + sqrt (12)  =  6 + 2sqrt (3)   = longer side of rectangle

 

cool cool cool

 Oct 12, 2023

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