Question

the side of a rhombus is 8 cm . if one of its diagonal measure 12 cm ,find the length of other diagonal and the area of the rhombus

Answer 1

Solution: we know that Diagonals of rhombus bisect each other...

So Apllying Pythagoras theorm..
8^2= 6^2+ x ^2

x^2= 25
x= 5.
so,required length of other diagonal is 5*2= 10 cm..

Area of rhombus= 1/2(d1*d2)

=> 1/2 ( 12 * 10 )
=> 60 sq. cm

I HOPE IT CLEARS YOUR DOUBTS

Answer 2

Hello!

Your Answer:

 The first diagonal will be bisected by the second one at 90 degrees.

Therefore, side will act as a hypotenuse.

Hypotenuse = 8cm

 8^2 = $6^{2} + (\frac{1}{2}diagonal_{2} )^{2}$

⇒  1/2 diagonal ^ 2 = 8 ^2 - 6^2 = 64 - 36 = 28

diagonal = 2$\sqrt{28}$ = 4$\sqrt{7}$

Area = 1/2 x diagonal1  x diagonal 2

1/2 x 12cm x 4$\sqrt{7}$

= 24$\sqrt{7}$ cm^2
I hope it helps you.

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