Question

Find the area of a rhombus whose side is$5cm$ and whose altitude is $4.8cm$. If one of the diagonals is $8cm$ long, find the length of the other diagonal.

Answer 1

Step 1: Find the required area:

The formula for the area of a rhombus when side and altitude are given is,

$\begin{array}{rcl}Area& =& Side\times height\end{array}$

So we can find the area of the rhombus as

$$\begin{gathered} A=5\times \times 4.8 \\ A=24c{m}^2 \end{gathered}$$

Step 2: Length of another diagonal:

Given, that the length of one diagonal is $8cm$.

Suppose, the length of another diagonal is $xcm.$

Hence,

Area $=\frac{8x}{2}$ [Since, Area $=$Products of diagonals$÷2$]

Area $=4x$

$\Rightarrow$$24=4x$

$\Rightarrow x=\frac{24}{4}$

$\Rightarrow x=6cm$

Hence, the area of the rhombus is $24{cm}^2$and the length of the other diagonal is $6cm.$