Question

The area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m is ...........

• A. $364m^2$
• B. $384m^2$
• C. $483m^2$
• D. $463m^2$

Answer 1

The correct option is B $384m^2$

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
$A=\frac{1}{2}\times 32\times 24$
$A=384m^2$
Answer (B) $384m^2$