Question

Find the area of a rhombus whose side is $6cm$ and whose altitude is $4cm$. If one of its diagonals is $8cm$ long, find the length of the other diagonal.

• A. $24c{m}^2,6cm$
• B. $24c{m}^2,8m$
• C. $4.4c{m}^2,6cm$
• D. $Noneofthese$

Answer 1

Answer: (A)

$24c{m}^2,6cm$

Let $ABCD$ be a rhombus of side $6cm$ and whose altitude $DE=4cm$. Also, one of its diagonals, $BD=8cm$.

Area of the rhombus $ABCD$

$=2\times Area\left(\Delta ABD\right)=2\times \frac{1}{2}\times AB\times DE$

$=(6\times 4)c{m}^2=24c{m}^2$

Also, area of the rhombus $ABCD$

$=\frac{1}{2}\times AC\times BD$

$\Rightarrow \frac{1}{2}\times AC\times 8=24$

$\Rightarrow AC=6cm$

Hence, the other diagonal is $6cm$.