Question

The diagonal of a rectangular plot is $34m$ and its perimeter is $92m$. Find its area.

• A. $480m^2$
• B. $380m^2$
• C. $310m^2$
• D. $580m^2$

Answer 1

The correct option is A $480m^2$

Let length be $am$ and breadth be $bm$.
Daigonal $=34m$
$=>a^2+b^2=(34{)}^2$
$=>a^2+b^2=1156$
Also,
$2(a+b)=92$
$=>(a+b)=46$
Area of rectangle $=\left(ab\right)m^2$
Now,we know,
$(a+b{)}^2=a^2+b^2+2ab$
$=>(46{)}^2=1156+2ab$
$=>ab=\frac{2116-1156}{2}$
$=\frac{960}{2}$
$=480$
Therefore,
Area $=480m^2$