Question

Find the altitude of a rhombus with perimeter $48cm$ and area $360c{m}^2$.

Answer 1

Step 1: Find the side of rhombus using its perimeter

We know that, perimeter of rhombus is ($4\times$side)

Let the side (base) of rhombus be $b$

Given, perimeter is $48cm$.

So,

$$\begin{gathered} P=4b \\ \Rightarrow 48=4b \\ \Rightarrow b=\frac{48}{4} \\ \Rightarrow b=12cm \end{gathered}$$

Step 2: Find the altitude of rhombus using its area

We know that, area of rhombus is, (base $\times$ height)

Let the altitude (height) of the rhombus be $h$

We are given the area of rhombus as $360c{m}^2$

So,

$$\begin{gathered} A=b\times h \\ \Rightarrow 360=12\times h \\ \Rightarrow h=\frac{360}{12} \\ \Rightarrow h=30cm \end{gathered}$$

Therefore, the altitude of the rhombus is $30cm$.