Diagonals & Areas

Geometry Level 3

The difference between the lengths of the diagonals of two squares is √32 cm and the difference between their areas is 64 sq.cm.

If the smaller square has side 'x' cm and the larger square has side 'y' cm,

Find x + y.


The answer is 16.

Ojasee Duble by Ojasee Duble , 19, India

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2 solutions

Marta Reece
Apr 16, 2017

Difference of diagonals: x 2 − y 2 = 32 = 4 2 x\sqrt{2}-y\sqrt{2}=\sqrt{32}=4\sqrt{2}

x − y = 4 x-y=4

Difference of areas: x 2 − y 2 = ( x + y ) ( x − y ) = 64 x^2-y^2=(x+y)(x-y)=64

x + y = 64 x − y = 64 4 = 16 x+y=\frac{64}{x-y}=\frac{64}{4}=16

Comparing x − y x-y and x + y x+y by adding the two equations: 2 x = 20 = > x = 10 2x=20 =>x=10

y = 16 − 10 = 6 y=16-10=6

x + y = 16 x+y=16

1 Helpful 0 Interesting 0 Brilliant 0 Confused

That was way faster than me method! :)

Ojasee Duble - 4 years, 1 month ago

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