Question

Q. A rhombus and a triangle are equal in areas. if the base and height of the triangle are 24.8 cm and 5.5 cm respectively and the length of one diagonal of the rhombus is 22 cm, find the length of other diagonal of the rhombus.​ ​

Answer 1

Ar(Triangle)=Ar(Rhombus)  ,

1/2 * Base * Height = Product of Diagonals / 2 , (By Deriving the formulas)

1 / 2 * 24.8 * 16.5  = 22 * x / 2 ,

204.6 = 22 * x / 2 ,

22x = 204.6 * 2 ,

x = 409.2 / 22 ,  

x = 18 . 6 .  

Length of diagonal = 18.6 .

Answer 2

Answer:

the length of other diagonal of the rhombus is 6.2 cm

Step-by-step explanation:

let's consider p &q diagonals of rhombus p=22cm

A(∆)= 1/2 base ×height=1/2 ×24.8×5.5=68.2

A(∆)=A(rhombus)=68.2= pq/2 =22q/2=11q

68.2/11=6.2=q

hence. q=6.2 cm