geometry

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the perimeter of a rhombus is 36 inches. if the longer diagonal is 14 inches what is the length of the shorter diagonal of the rhombus?

• geometry -

so each side is 9 inches.

A property of a rhombus is that its diagonals right-bisect each other

Let the other diagonal be 2y inches, so we have
4 congruent right-angled triangles with sides 7 and y and hypotenuse of 9

y^2 + 7^2 = 9^2
y^2 = 32
y = √32 = 4√2

so the other diagonal is 8√2

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