Question

5.If the sum of the lengths of the diagonals of a rhombus is 10 m and if its area is 9 m2. Then, what is the sum of squares of the diagonals?

Answer 1

Answer:

Sum of lengths of diagonal is 10.

i.e. a+b=10.

Area of rhombus is given by 1/2(a)(b)=9.

Now

(a+b)^2= a^2 + b^2 + 2ab

=> a^2 + b^2 = (a+b)^2 - 2ab

= 10^2 - 2*18 ( ab = 9*2)

= 100 - 36

= 64