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

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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.

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