Perimeter of a rhombus is 146cm and one diagonal is 55cm. Find the other diagonal and area of a rhombus.

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Solution

Firstly.. side of rhombus..
4×side=146
Side= 36.5cm

Now..
By applying Pythagoras theorem in one of the triangle formed by joining two diagonals..

36.5 square = 27.5 square + half diagonal . square
1332.25 - 756.25 = half diagonal's square
24 = half diagonal

So.. Second diagonal = 24×2
48m
Now..
Area of rhombus = 1/2 × d1 × d2
= 1/2 × 55 × 48
= 1320 cm square

hope it helps

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