Question

8. Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.

Answer 1

Step-by-step explanation:

Area of the rhombus = Side × Length of the altitude 

= 5*4.8

= 24 sq cm 

Now,

Let the length of the other diagonal = x

It is known that the area of a rhombus is half the product of its diagonals. 

∴ (1/2) × 8 × x = 24

⇒ 4x = 24

⇒ x = 6 cm

The length of the other diagonal is 6 cm.

Answer 2

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

Formula of area of rhombus =Base×Altitude

Putting values, we have

Area of rhombus =5×4.8=24

Since, Area of rhombus is 24 cm².

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

Given,Length of one diagonal =$d_1$=8

Let length of other diagonal =$d_2$

After substituting the values, we get

$24=\frac{1}{2}×8×d_2$

$24=4×d_2$

$4×d_2=24$

$d_2=\frac{24}{4}$

$d_2=6$

Hence, length of other diagonal is 6 cm.