Question

If each side of the rhombus is 25 and the diagonal 30 cm. Find the height. Pleases answer with explanation

Answer 1

Given :-

Each side of rhombus = 25cm

One diagonal = 30 cm

Solution :-

As we know that ,

A = 1/2 √(d1)^2 + (d2)^2

Here , A is the side of rhombus ,

d1 = diagonal 1 , d2 = diagonal 2

Therefore ,

25 = 1/2 √ (30)^2 + ( d2)^2

50 = √ (30)^2 + ( d2)^2

(50)^2 = 30^2 + d2^2

(d2)^2 = (50)^2 - (30)^2

(d2)^2 = 2500 - 900

(d2)^2 = 1600cm^2

d2 = 40 cm

Hence , The area of rhombus

= 1/ 2 * d1 * d2

The area of rhombus = 1/2 * 30 * 40

The area of rhombus = 600 sq.cm

Now ,

The height of the rhombus = Area / base

The height of the rhombus = 600 / 25

The height of the rhombus

= 24 cm