Area of a rhombus is 25cm² and one of the diagonal is double the other in length find the sum of the two diagonals

Answer 1

Let the smaller diagonal be x cm. Then the larger diagonal would be 2x cm because it is double the length of the smaller diagonal.

The area of a rhombus can be calculated using the formula:

Area = (d1 * d2) / 2

where d1 and d2 are the diagonals of the rhombus.

Given that the area is 25 cm², we have:

25 = (x * 2x) / 2
25 = 2x^2 / 2
25 = x^2
x^2 = 25
x = 5

So, the smaller diagonal is 5 cm and the larger diagonal is 10 cm.

To find the sum of the two diagonals:

Sum = 5 + 10
Sum = 15

Therefore, the sum of the two diagonals is 15 cm.