Question

diagonals of a rhombus are in the ratio 3:4 perimeter is 40 cm find the length of the diagonals

Answer 1

hiii!!!

here's ur answer...

given the perimeter of the rhombus is 40cm.

therefore side × 4 = 40cm

==> side = 40/4

==> side = 10cm

now,

given that the diagonals are in ratio 3:4.

let the diagonals be 3x and 4x.

we know that the diagonals of a rhombus bisect each other in the centre.

let hypontuse be the side of the rhombus.

by Pythagoras thereom:-

a² + b² = c²

==>(3x/2)² + (4x/2)² = 10²

==> 9x²/4 + 16x²/4 = 100

==> 9x²+16x²/4 = 100

==> 25x²/4 = 100

==> x²/4 = 100/25

==> x²/4 = 4

==> x² = 4 × 4

==> x² = 16

==> x = √16

==> x = 4cm

hence, diagonals of the rhombus are:-

→ 3x = 3 × 4

= 12cm

→ 4x = 4 × 4

= 16cm

hope this helps u..!!