Question

the area of rhombus is 93.5 cm². if it's perimeter is 44 cm , then find its altitude​

Answer 1

Answer :

• Altitude of rhombus is 8.5cm

Given :

• Area of rhombus is 93.5 cm²
• Perimeter is 44cm

To find :

• Altitude

Solution :

First we need to find the sides

We know that

• Perimeter of rhombus = 4 × s

Given, perimeter is 44cm so,

⟾ Perimeter = 4 × s

⟾ 44 = 4 × s

⟾ s = 44/4

⟾ s = 11 cm

Hence , Sides is 11cm

Now , Finding the altitude :

• Let the altitude be h (height)

We know that

• Area of rhombus = base × height

Given,

• Area of rhombus is 93.5 cm²
• Base is 11cm

⟾ Area of rhombus = base × height

⟾ 93.5 = 11 × height

⟾ 935/10 = 11 × height

⟾ height = 935 / 10 × 11

⟾ height = 935/110

⟾ height = 8.5cm

Hence , Altitude of rhombus is 8.5cm

Answer 2

$\underline{\underline{\sf{\maltese\:Given\::-}}}$

• Area of rhombus is 93.5 cm²
• Perimeter is 44cm

$\underline{\underline{\sf{\maltese\:To\:find\::-}}}$

• The altitude of the rhombus

$\underline{\underline{\sf{\maltese\:Concept:-}}}$

$\odot$ Here we have the area of the rhombus and its perimeter, so to find the altitude of the rhombus we need base and the base of the rhombus is equal to the side of the rhombus, so firstly we will find out the base of the rhombus.

$\odot$ After finding the base of the rhombus we will find out the altitude of the rhombus.

$\underline{\underline{\sf{\maltese\:Solution:-}}}$

$\bigstar$ Let us find out the base of the rhombus by applying the formula                     ( Perimeter of the rhombus = 4 × s )

$\qquad\sf{:\implies\:Perimeter\:of\:the\:rhombus\:=\:4\:\times\:s}$

$\qquad\sf{:\implies\:44\:=\:4\:\times\:s}$

$\qquad\sf{:\implies\:\dfrac{44}{4}\:=\:s}$

$\qquad\sf{:\implies\:s\:=11\:cm}$

Hence the base of the rhombus is 11 cm.

$\bigstar$ Let us find out the altitude of the rhombus by substituting the values in the formula ( Area of the rhombus = Base × Height )

$\qquad\sf{:\implies\:Area\:of\:rhombus\:=\:Base\:\times\:height}$

$\qquad\sf{:\implies\:93.5\:=\:11\:\times\:height}$

$\qquad\sf{:\implies\:\dfrac{935}{10}\:=\:11\:\times\:height}$

$\qquad\sf{:\implies\:height\:=\:\dfrac{935}{10\:\times\:11}}$

$\qquad\sf{:\implies\:height\:=\:\dfrac{935}{110}}$

$\qquad\sf{:\implies\:height\:=\:8.5\:cm}$

Hence the altitude of the rhombus is 8.5 cm