Question

Find the area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m.
​

Answer 1

Answer:

Perimeter = 80 m,

So, length of a side =80/4=20m,

and Diagonal of a rhombus = 24m,

As, we know that,

The halves of diagonals and a side of a rhombus from a right angled triangle with side as hypotenuse.

Let the length of the other diagonal =2x.

x

2

+(24/2)

2

=20

2

=x

2

+144=400

x

2

=400−144=256

x=16

The measure of the another diagonal of the rhombus = 2*16 =32 m

So, Area of the rhombus =1/2*Diagonal of a rhombus*Measure of the another diagonal

A=

2

1

×32×24

A=384m

2

Answer 2

Answer:

Perimeter = 80 m,

So,  length of a side =80/4=20m,

 and Diagonal of a rhombus = 24m,

 As, we know that,

The halves of diagonals and a side of a rhombus from a right angled triangle with side as hypotenuse.

Let the length of the other diagonal =2x.

x2+(24/2)2=202=x2+144=400

x2=400−144=256

x=16

The measure of the another diagonal of the rhombus = 2*16 =32 m

So, Area of the rhombus =1/2*Diagonal of a rhombus*Measure of the another diagonal 

A=21×32×24

A=384m2

Answer is 384m2