Question

Q1.Ex. (2) Area of a rhombus is 96 sq cm. One of the diagonals is 12 cm find the
length of its side.​

Answer 1

Explanation:

Given

Area of a rhombus is 96 sq.cm

One of its Diagonal is 12cm

To Find

we have to find the length of its sides

$\sf\huge {\underline{\underline{{Solution}}}} </p><p>Solution</p><p>$

Since , we don't know the length of the other diagonal so,we firstly find it by using formula of area of rhombus.

Area of Rhombus= D1 * D2 ÷ 2

Where ,D1 & D2 are two Diagonals

Area of Rhombus= 12*D2

=> 96 = 12*D2

=> D2= 96/12

=> D2= 8

Hence,length of the other diagonal is 8cm

See the figure in attachment:↥

Let AC and BD be the two Diagonals of rhombus with length 12cm &8 ck respectively.

Since, we know that Diagonals of rhombus bisects each other at 90° or right angles.

By using the property:

AO= AC÷ 2 = 12÷2= 6cm

BO=BD÷2= 8÷2= 4cm

Now,in ∆AOB

By using Pythagoras theorem:

AB²= AO²+BO²

AB²= 6²+4²

AB²= 36+16

AB²= 52

AB= √52= 2√13cm

Therefore,the length of its side is 2√13cm

Answer 2

Answer:

Given that

Area= 96cm square

1/2×d1 × d2 = 96

. 6×d2 = 96

d2= 16cm