Question

find the length of the long diagonal of a rhombus when it's area of 24 square centimeters and it's short diagonal is 4 centimeters​

Answer 1

12

Explanation:

A rhombus is a parallelogram with all four sides equal.

Its diagonals are perpendicular.

Each of the triangles formed by the diagonals and the sides are congruent, so the area of the rhombus is 4 times the area of one of the triangles.

Since the short diagonal is given as 4, each of the triangles can be viewed as having a base of 2. Each triangle's height, h, then is one half the length of the long diagonal.

The are of one of the triangles is 1/2 (base)(height)=(1/2)(2)h

The area of the rhombus is then

4(1/2)(2)h=24

Solving for h gives

h=6

This makes the length of the long diagonal 2h=12