Question

The area of a rhombus is equal to the area of a triangle whose base and the corresponding height are 24.8 cm and 16.5 cm respectively. If one of the diagonals of the rhombus is 22 cm, find the lenght of the other diagonal.

Answer 1

Area of a triangle = $\frac{1}{2}$ $\times$ Base $\times$ Height
= $\left(\frac{1}{2}\times 24.8\times 16.5\right)$ cm² = 204.6 cm²
Given:
Area of the rhombus = Area of the triangle
Area of the rhombus = 204.6 cm²

Area of the rhombus = $\frac{1}{2}$ $\times$ (Product of the diagonals)
Given:
Length of one diagonal = 22 cm
∴ Length of the other diagonal = $\left(\frac{204.6\times 2}{22}\right)$ cm
= 18.6 cm