Question

The area of a rhombus, one of whose diagonals measures $8cm$ and the side is $5cm$, is

• A. $25{cm}^2$
• B. $24{cm}^2$
• C. $24.5{cm}^2$
• D. $26{cm}^2$

Answer 1

Answer: (B)

$24{cm}^2$

Let $h$ be the altitude and $y$ be the distance from $B$ to $O$.
By Pythagoras theorem,
$(5+y{)}^2+h^2=8^2$ ....(1)
Also, $y^2+h^2=5^2$ ...(2)

From (1) and (2),
$y=\frac{7}{5}$
Substituting value of $y$ in equation (2) we get,

$h=\frac{24}{5}$
Since, Area of rhombus $=$ Altitude$\times$ Base

$\therefore$ Area of Rhombus $=\frac{24}{5}\times 5=24{cm}^2$

Hence, option B.