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# Geometry

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The area of a square equals the square of a length of the side of the square. The perimeter of a square equals the sum of the lengths of all four sides. The sum of the areas of two squares is 65, while the difference in their areas is 63. Find the sum of their perimeters.

Jan 4, 2022

#1
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Let  x  equal the length of a side of the larger square.

Let  y  equal the length of a side of the smaller square.

x2 + y2  =  65

x2 -  y2  =  63

Adding these equations together:  2x2  =  128     --->     x2  =  64

The length of the larger square is 8.

Substituting:  x2 + y2  =  65     --->      82 + y2  =  65     --->     y2  =  1

The length of the smaller square is 1.

Find the perimeter of each square and add these lengths together.

Jan 4, 2022
#2
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The area of a square equals the square of a length of the side of the square. The perimeter of a square equals the sum of the lengths of all four sides. The sum of the areas of two squares is 65, while the difference in their areas is 63. Find the sum of their perimeters.

The sum of the areas of two squares is 65     x2 + y2  =  65

while the difference in their areas is 63     x2 – y2  =  63

Add the two together                                            2x2  =  128

x2  =  64

x   =  8    so the perimeter of this square is 32

x2 + y2  =  65

64 + y2  =  65

y2  =  65 – 64  =  1

y   =  1   so the perimeter of this square is 4

total of the two perimeters is 32 + 4  =  36

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Jan 4, 2022