Question

If the area of the Rhombus is 60 sq.cm and one of the diagonals is 8 cm, find the length of the other diagonal ​

Answer 1

Length of other diagonal = 15 cm

$\orange{\bigstar}$  Given  $\green{\bigstar}$

→ Area of the rhombus is 60 sq.cm

→ One of the diagonal of rhombus is 8 cm

$\orange{\bigstar}$  To Find  $\green{\bigstar}$

Length of the other diagonal

$\orange{\bigstar}$  Formula Applied  $\green{\bigstar}$

Area of the parallelogram is given by half of the product of diagonals

$\red{\bigstar}\ \; \bf Area=\dfrac{1}{2}\times (D_1.D_2)$

where ,

• D₁ denotes Diagonal 1
• D₂ denotes Diagonal 2

$\orange{\bigstar}$  Solution  $\green{\bigstar}$

Given ,

Area of the rhombus = 60 sq.cm

Length of Diagonal 1 = 8 cm

Length of Diagonal 2 = D₂ cm

Apply formula ,

$\bf A=\dfrac{1}{2}\times (D_1.D_2)\\\\\to \rm 60=\dfrac{1}{2}\times (8.D_2)\\\\\to \rm 60=4D_2\\\\\to \rm 15=D_2\\\\\to \bf D_2=15\ cm\ \; \pink{\bigstar}$

So , Length of the other diagonal is 15 cm

Answer 2

Given :-

• The area of the Rhombus is 60 sq.cm
• One of the diagonals is 8 cm

To Find :-

• The length of the other diagonal 

Formula :-

$\blue{\boxed{\sf Area=\dfrac{1}{2}\times (D_1.D_2)}}$

Where,

• D₁ denotes Diagonal 1
• D₂ denotes Diagonal 2

We have,

$\blue{\boxed{\sf Area=\dfrac{1}{2}\times (D_1.D_2)}}$

Substitute the given values we get,

$\red{\sf Area=\dfrac{1}{2}\times (D_1.D_2)}\\\\\green{\implies \sf 60=\dfrac{1}{2}\times (8.D_2)}\\\\\pink{\implies \sf 60=4D_2}\\\\\purple{\implies \sf 15=D_2}\\\\\blue{\implies \boxed{\sf D_2=15\ cm}}</p><p>$

$\large{\gray{\therefore\underline{\sf Length \: of \: the \: other \: diagonal \: is \: 15 cm}}}$