Rhombus ABCD has perimeter 148, and one of its diagonals has length 24. How long is the other diagonal?

70 units.

Step-by-step explanation:

The 4 sides of a rhombus are equal so each side has length 148 / 4

= 37 units. The diagonals bisect each other at right angles so when we draw the 2 diagonals we have 4 congruent right-angled triangles.

So consider one of these triangles:

The hypotenuse is 37 units and one of the legs = 1/2 * 24 = 12 units (half of the diagonal of length 24).

So the other leg is found using Pythagoras:

x^2 = 37^2 - 12^2 = 1225

x = 35.

This is half of the other diagonal so the latter = 70 units.