posted by mc .
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?
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