Question

of the diagonals of rhombus of the side are 15cm are in ratio 3:4, find the area of rhombus

Answer 1

Solution :-

The side of rhombus = 15 cm

Ratio of two diagonals = 3 : 4

The rhombus is formed of 4 right angled triangles. Our basic Pythagoras Triplet is 3 : 4 : 5

Since, the hypotenuse in this case is 15 cm (that is 5 × 3 = 15), the other two sides of the right angled triangle will be 9 (3 × 3 = 9) and 12 (4 × 3 = 12).

9 : 12 : 15 is also a Pythagoras Triplet.

These sides of the right triangle are half the entire diagonal, so the two diagonals are -

9*2 = 18 cm and 

12*2 = 24 cm

So, the two diagonals are 18 cm and 24 cm respectively..

Now, 

Area of the given rhombus = (Diagonal 1 × Diagonal 2)/2

⇒ (18*24)/2

⇒ 432/2

= 216 sq cm

Answer.