Question

Find the area of a rhombus whose side is 12 cm and altitude is 8 cm. If one of the
diagonal is 16 cm long , find the length of the other diagonal.​

Answer 1

Since,a rhombus is also a kind of a parallelogram.

Formula of area of rhombus =Base×Altitude

Putting values, we have

Area of rhombus =12×8=96

Since, Area of rhombus is 96 cm².

Also,formula for area of rhombus =$\frac{1}{2}×d_1d_2$

Given,Length of one diagonal =$d_1$=16

Let length of other diagonal =$d_2$

After substituting the values, we get

$96=\frac{1}{2}×16×d_2$

$96=8×d_2$

$8×d_2=96$

$d_2=\frac{96}{8}$

$d_2=12$

Hence, length of other diagonal is 12 cm.

Answer 2

Answer:

Since,a rhombus is also a kind of a parallelogram.

Formula of area of rhombus =Base×Altitude

Putting values, we have

Area of rhombus =12×8=96

Since, Area of rhombus is 96 cm².

Also,formula for area of rhombus =\frac{1}{2}×d_1d_221×d1d2

Given,Length of one diagonal =d_1d1 =16

Let length of other diagonal =d_2d2

After substituting the values, we get

96=\frac{1}{2}×16×d_296=21×16×d2

96=8×d_296=8×d2

8×d_2=968×d2=96

d_2=\frac{96}{8}d2=896

d_2=12d2=12

Hence, length of other diagonal is 12 cm.