Question

The area of the given field is $3500m^2$, $AF=25m,AG=50m,AH=75m$ and $AB=100m$. The rest of the dimensions are shown in the figure. Find the value of $x$.

• A. $17m$
• B. $20m$
• C. $22m$
• D. $25m$

Answer 1

The correct option is B $20m$

Total area $=$ Area of $\Delta AFC+$ Area of $\Delta AGD+$ Area of trapezium $FCEH+$ Area of $\Delta BHE+$ Area of $\Delta DGB$

$=\frac{1}{2}\times AF\times FC+\frac{1}{2}\times AG\times DG$ $+\frac{1}{2}\times BH\times HE+\frac{1}{2}\times BG\times DG$ $\Rightarrow \frac{1}{2}\times 25\times 20+\frac{1}{2}\times 50\times 40+\frac{1}{2}\times (20+x)\times 50$ $+\frac{1}{2}\times 25\times 20+\frac{1}{2}\times 50\times 40+\frac{1}{2}\times (20+x)\times 50$

$\Rightarrow 250+1000+(20+x)25+12.5x+1000-3500$

$\Rightarrow 2250+500+25x+12.5x=3500$

$\Rightarrow 37.5x-3500-2750-750$

$\Rightarrow x=\frac{750}{37.5}=20m$