Question

The area of a rohumbus is 93.5 cm² . if its perimeter is 44 cm , then find its altitude.​

Answer 1

perimeter is 44 a=11 area =93.5

Answer 2

Given -

• Area of rhombus = 93.5cm²

• Perimeter of rhombus = 44cm

To find -

• Altitude of the rhombus

Formulae used -

• Perimeter of rhombus

• Area of rhombus

Solution -

In the question, we are provided with the area of the rhombus and the perimeter of the rhombus, and we need to find the altitude of the rhombus, for that, first we will, find the base and then, we will use the formula of altitude of the rhombus, by dividing area by base. From that, we will obtain the altitude of the rhombus. Let's do it!

According to question -

First we will the base of the rhombus, by using the formula of the perimeter of the rhombus. For that we need, sides of the Rhombus, and we should multiply it with 4, but sides area not given, and perimeter is given, so we will, divide, perimeter with 4.

${\sf{ \underline{perimeter = 4s}}}$

On substituting the values -

$\sf \: p = 4s \\ \\ \\ \sf \: 44cm = 4s \\ \\ \\ \sf \: 4 = \cancel \dfrac{44}{4} \\ \\ \\ \sf \: s = 11$

Now -

We will find the altitude of the rhombus, by dividing, the area of the rhombus by the base, we have obtained, from that, whatever value we will get, that is going to be the altitude of the rhombus.

$\sf \underline{altitude = \dfrac{area}{base}}$

On substituting the values -

$\sf{Area\:of\:rhombus=b\times h}$

$\\ \sf{93.5 = 11 \times h}$

$\\ \sf{h = \dfrac{93.5}{11}}$

$\\ \sf{h = 8.5\:cm}$

$\therefore$ Altitude of the rhombus is 8.5cm

________________________________________________