Question

Area of rhombus is 24cm² and one of the diagonal is triple the other in length find the sum of the two diagonals

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the sum of the two diagonals of a rhombus, we first need to find the lengths of the two diagonals.

Let the shorter diagonal be x cm. Therefore, the longer diagonal will be 3x cm.

The area of a rhombus is given by the formula:

Area = (1/2) * d1 * d2

where d1 and d2 are the lengths of the diagonals.

Given that the area of the rhombus is 24 cm², we can substitute the values into the formula:

24 = (1/2) * x * 3x
24 = (3/2) * x²
x² = 16
x = 4 cm

Therefore, the shorter diagonal is 4 cm and the longer diagonal is 3 * 4 = 12 cm.

The sum of the two diagonals is:
4 + 12 = 16 cm

So, the sum of the two diagonals of the rhombus is 16 cm.