Question

Find the area of a rhombus whose side is 6.5 cm and altitude is 5 cm. If one of its diagonal is 13 cm, find the length of another diagonal. (i) by heron's rule and (ii) by construction.

Answer 1

Answer:

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

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