Question

Find the area of a rhombus whose side is 8cm and who's altitude I'd 5cm. if one of its diagonal is 10cm long ,find the length of the other diagonal​

Answer 1

Answer:

Area of rhombus = Base × Height =21×Product of diagonals

⇒5×4.8=21×(8×x)

⇒24=21×(8×x)

⇒x=6 cm

Answer 2

Given: Side of Rhombus = 8cm.

Altitude of Rhombus= 5cm.

Diagonal of Rhombus = 10 cm.

To Find: Length of another Diagonal =?

Solution:

Let the diagonals of the rhombus be D1 and D2 respectively.

d1= 10cm

Area of Rhombus =

$\frac{d1 \times d2}{2}$

Rhombus is also considered to be a parallelogram ( parallelogram property)

Therefore, let the given side of the rhombus be (b) and the given altitude of the rhombus be (h).

Since rhombus is a parallelogram,

Area of Rhombus = Area of Parallelogram

$\frac{d1 \times d2}{2} = b \times h$

$\frac{10 \times d2}{2} = 5 \times 8$

$5 \times d2 = 40$

$d2 = \frac{40}{5}$

$d2 = 8$

The Length of the other diagonal is 8cm.