Question

The cross section of a canal is in the shape of trapezium. The canal is $15m$ wide at the top and $9m$ wide at the bottom. If the area of the cross section is $720m^2$, then the depth of the canal is

• A. $55m$
• B. $50m$
• C. $58.5m$
• D. $60m$

Answer 1

The correct option is D $60m$

Given,

The canal is $15m$ wide at the top and $9m$ wide at the bottom.

Area of the cross section$=720m^2$

Let the depth of the canal be $h$

Area of a trapezium $=\frac{1}{2}\times$ Sum of parallel sides $\times$ height

$\Rightarrow 720=\frac{1}{2}\times (9+15)\times h$

$\Rightarrow 720=\frac{24\times h}{2}$

$\Rightarrow h=\frac{720\times 2}{24}$

$\Rightarrow h=60$

Hence, depth of the canal is $60m$.