Question

rhombus is in ratio 3 is to 4 if its perimeter is 40 cm find the length of the sides and diagonals of the Rhombus

Answer 1

The diagonals of a rhombus intersect at right angles, so, together with the sides of the rhombus, the diagonals will make four right triangles with their ratio of sides 3:4:5. We can let the sides of these triangles be 3x, 4x, and 5x, and since the perimeter is 40, we know each side is 10, so 5x=10, and x=2.

The four triangles measure 6, 8, 10, and each diagonal is composed of two short legs of the right triangles or two long legs. The short legs are 6, so the short diagonal is 12. The long legs are 8, so the long diagonal is 16.