Question

The area of a rhombus is 96cm square. If one of its diagonals are 16 cm, then the length of its sides are what?

Answer 1

base =6  height=16 because area is product of altitude and height then altitude equals to area divided by height

Answer 2

Solution:-

• given:-

1)The area of rhombus is 96cm square .

2) one diagonal is 16 cm.

we know all side of rhombus are equal.

let, bd = 1st diagonal = 16 cm and

ac = 2cd diagonal ,

A = Area = 96cm.

=> Area of rhombus = [ac×bd]/2

=> A = [ac×bd]/2

=> 96 = [ ac × 16 ]/2

=> 96×2 = ac × 16

=> 192 = ac × 16

=> bd = 192/16

=> bd = 12 cm

•we know,

ac = ao + oc and bd = bo + od

• diagonals of a rhombus bisect each other at an angle of 90° or right angle.

means ao = oc = 12/2 = 6 cm &

bo = od = 16/2 = 8 cm.

in Δ aod

by Pythagoras theorem

=> (ad)² = (ao)² + (od) ²

=> (ad)² = (6)² + (8) ²

=> (ad)² = 36 + 64

=> (ad)² = 100

=> ad = √100

=> ad = 10 cm

Hence all side of rhombus are 10 cm.

i hope it helps you .