Question

If area of rhombus is 720 and one side 41 then find sum of diagonals

Answer 1

HELLO DEAR,

GIVEN:-

Area of the rhombus = 720m².

We know that Area of the rhombus = (d1 * d2)/2

where, d1 and d2 are the diagonals of rhombus

720 = (d1 * d2)/2

=  1440 = d1 * d2 -----------( 1 )

now,Given

Side of a rhombus = 41m.

We know that (Side)² = (d1/2)² + (d2/2)²

=  (41)² = (d1/2)² + (d2/2)²

=  1681 = (d1/2)² + (d2/2)²

=  1681 * 4 = (d1)² + (d2)²

=  6724 = (d1)² + (d2)².

= 6724 + 2(d1 * d2) - 2(d1 * d2) = (d1)² + (d2)²

= 6724 + 2(1440) = (d1)² + (d2)² + 2(d1 * d2)

= 6724 + 2880 = (d1 + d2)²

[as,  (a + b)² = a² + b² + 2ab]

= (d1 + d2)² = 9604

= (d1 + d2)² = √{9604}

= (d1 + d2) = 98cm

Therefore, the sum of diagonal of the rhombus = 98m.

I HOPE ITS HELP YOU DEAR,

THANKS