Question

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

Answer 1

Step 1: Find the area of the given Rhombus:

Given:

Side of Rhombus $=5cm$ (base)

Altitude $=4.8cm$ (height)

Diagonal $d_1=8cm$

We know, Area of the Rhombus $=$ Base $\times$ height

$=5\times 4.8c{m}^2$

$=24c{m}^2$

Therefore, Area of given rhombus is $24c{m}^2$.

Step 2: Length of the other diagonal:

we know, For a rhombus having diagonal $d_1$ and $d_2$,

Area $=\frac{1}{2}\times d_1\times d_2$

$$\begin{gathered} \Rightarrow 24=\frac{1}{2}\times 8\times d_2 \\ \Rightarrow d_2=\frac{24\times 2}{8} \\ \Rightarrow d_2=6c{m}^{} \end{gathered}$$

Hence, the length of the other diagonal $d_2$ is $6$ cm.