Question

Find the area of the rhombus whose side is 6.5cm and altitude is 5cm. If one of the diagonal is 13 cm long, find the length of other diagnol

Answer 1

Answer :-

The length of the other diagonal is 5 cm.

Solution :-

We know that Rhombus is also a Parallelogram.

When we consider Rhombus as a Parallelogram

Base of the Parallelogram (b) = 6.5 ccm

Altitude of the Parallelogram (h) = 5 cm

Area of the Parallelogram = bh

= 6.5 * 5

= 32.5 cm²

When we consider Rhombus

Length of one of the diagonal of the Rhombus (d1) = 13 cn

Let the length of the another diagonal be 'd2' cm

Area of the Rhomus = Area of the Parallelogram

⇒ d1 * d2/2 = 32.5 cm²

⇒ 13d2/2 = 32.5

⇒ 13d2 = 32.5 * 2

⇒ 13d2 = 65

⇒ d2 = 65/13

⇒ d2 = 5 cm

Therefore the length of the other diagonal is 5 cm.

Answer 2

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Area of parallelogram = 6.5 ×5 = 32.5cm^2.

We have,

Area of Parallelogram = Area of Rhombus.

ie, d1 × d2/2 = 32.5cm^2.

13d2 = 65.

d2 = 65/13

d2 = 5 cm.