Question

the perimeter of rhombus is 200m. if one of the diagonal is 80m, find the length of the other diagonal and area of the rhombus

Answer 1

Let side of the rhombus be 's' and diagonals be d and d'

Given , perimeter of rhombus=200m

➡4s= 200

➡s=50 m

Also given , d'=80m

We know , diagonals of a rhombus are perpendicular bisectors.

➡(d/2)²+(d'/2)²=s²

➡(d/2)²=900

➡d=2*30=60 m

Area of the rhombus = d*d'/2 = 60*80/2 = 2400 m²

 

There’s an alternate method too:


Area of rhombus is half the length of one diagonal times the length of the other. 
A side length is 200/4 = 50m 
if x and y are the half lengths of the diagonals 
then sqrt(x² + y²) = 50 
x² + y^2 = 2500 
If one of the diagonals is 80m, then 1/2 of this is 40m 
40^2 + y² = 2500 
1600 + y² = 2500 
y² = 900 
y = 30 so the other diagonal is 60m 

The area is therefore 30*80 = 2400 m²

Or,

Let’s make the side of the rhombus be 's' and diagonals be d and d'

Given , perimeter of rhombus=200m

4s= 200

s=50 m

Also given , d'=80m

We know , diagonals of a rhombus are perpendicular bisectors.

(d/2)²+(d'/2)²=s²

(d/2)²=900

d=2*30=60 m

Area of the rhombus = d*d'/2 = 60*80/2 = 2400 m²

 

Hope This Helps :)