Rhombus ABCD has perimeter 148, and one of its diagonals has length of 24. How long is the other diagonal?
(1/4) of the perimeter = a side length
148 * (1/4) = 37
The side length forms the hypotenuse of a right triangle
And (1/2) of the known diagonal length = 12 forms one leg of this triangle
So...using the Pythagorean Theorem, the other leg =
sqr ( 37^2 - 12^2 ) = sqrt ( 1369 - 144) = sqrt ( 1225) = 35
And twice this is the length of the other diagonal = 70