Question

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

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

$\sf\huge {\underline{\underline{{Solution}}}}$

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:

length of its side is 10cm

Step-by-step explanation:

Area of a rhombus = 96sq cm.

Area of a rhombus. = 1/2×d1×d2 sq units

diagonal (d1) = 12cm

diagonal (d2) = ?

1/2 × 12 × d2 = 96

6× d2 = 96

d2 = 96/6

d2.= 16 cm.

In rhombus the diagonals perpendicular meet together. they form right angles.

base = d1/2 = 12/2 = 6cm

height =d2/2 = 16/2 = 8 cm

length of its side = √8^2 + 6^2

= √8×8 + 6×6

= √64+36

= √100

= 10cm.