Question

The diagonals of a rhombus are in the ratio 3 ratio 4 and the area is 54 CM find the side of the Rhombus

Answer 1

Step-by-step explanation:

The area of the rhombus is 1/2(D1)(D2). It is given that the diagonals D1 and D2 are in the ratio 3:4 hence the lengths of diagonals D1 and D2 are 3k and 4k. 1/2(3k)(4k)=54 =>

12k^2=108=>k^2=9 =>k=3. So the length of diagonals are 9cm and 12cm. Side of the rhombus =>

$\sqrt{ {9}^{2} + {12}^{2} } = > \sqrt{81 + 144} = > \sqrt{225}$

$= > 15cm$

Hope it helps you.

Answer 2

Step-by-step explanation:

Let the diagonals be 8y and 6y.

Then area of rhombus = 4 × 0.5 × 4y × 3y =54

Solving y = 3/2

Side of rhombus is equal to 5y.

So 5×3/2 = 7.5

Side of rhombus = 7.5