Question

I'd diagonals of rhombus are in the ratio 4 : 3 and side of rhombus is 25m. Find the length of the diagonals

Answer 1

Answer:

Let diagonals be AC and BD intersect ay O

Now AC : BD=4:3

AC/2:BC/2=4:3

AO:BO=4:3

AO=4k

BO=3k

Now as we know diagonals of rhombus bisect each other at 90 degree

ΔAOB is a rt angle

∴ By pythagoras theorem

AO^2+BO^2=25^2

(3k)^2+4k^2=625

9k^2+16k^2=625

25k^2=625

k^2=25

k=5

Now AO=4k=20

BO=3k=15

AC=2 AO=40 cm

BD=2 BO=30 cm

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