Question

The area and a diagonal of a rhombus are 60^2 and 12cm respectively. Calculate the length of the other diagonal

Answer 1

Step-by-step explanation:

⭐Question:-

The area and a diagonal of a rhombus

are 60^2 and 12cm respectively.

Calculate the length of the

other diagonal.

⭐Answer:-

✯Solution:-

The smallest diagonal of a rhombus

which has

60 degrees angles and one side as 12 cm, will be 12 cm. This is because the rhombus is actually two equilateral triangles with a common base.

The longer diagonal will be = 2 *12* sin 60 = 20.78460969 cm.

The area of the rhombus will be = d1*d2/2

=12*20.78460969/2 =124.7076581 sq cm.

Let us see the alternate solution:

The rhombus is a cluster of 4 right angle triangles.

So if one side of the rhombus, which is the same as the hypotenuse of the RAT = 12 cm,

the angles of the RAT are 30 deg

and 60 deg.

The longer side of the RAT = 12 cos 30 = 10.39230485 cm,

so the longer diagonal will be 2*10.39230485

= 20.78460969 cm.

The shorter side of the RAT = 12 cos 60 = 6 cm,

so the shorter diagonal will be 2*6 = 12 cm.

✿Hence, the answer is 12 cm.