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Question

The diagonals of a rhombus are in the ratio 3:4. If its perimeter is 40 cm, find the length of the sides and diagonals of the rhombus.

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Solution

R.E.F image
Let the sides of rhombus be a
and diagonals be d1 and d2
perimeter =40cm

4a=40cm

a=10cm

Ratio of diagonals=3:4

d1d2=34

d1=3d24 ...(1)

Now,
a2=d214+d224

d21+d22=4a2

9d2216+d22=4(10)2

25d2216=400

Square Rooting both sides

5d24=20

d2=16

put d2=16 in equation ...(1)

d1=12

1180198_1284168_ans_f893cb7986cb489a9c567be686008bea.jpg

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