Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The measurements of a field To B (in metres) are as shown 400 100 to E If the total area of the field is 300 x to D 27500 sq. m, then the value of 50 to C 200 100 x is equal to From A
(a)25 m
(b)30 m
(c)50 m
(d)75 m 714
Answer
Answer (as printed): A
Explanation
The field may be drawn as shown in the adjoining figure. We have: $\mathrm{AB}=400 \mathrm{m}, \mathrm{AF}=300 \mathrm{m}, \mathrm{AG}=200 \mathrm{m}$, $\mathrm{AH}=100 \mathrm{m}, \mathrm{EF}=100 \mathrm{m}, \mathrm{CH}=50 \mathrm{m}, \mathrm{DG}=x$ metres. Area of the field $$\begin{aligned} = & \operatorname{ar}(\triangle A G D)+\operatorname{ar}(\triangle B G D)+\operatorname{ar}(\triangle B F E)+\text { ar }(\text { trap } C E F H) \\ + & \operatorname{ar}(\triangle A H C) \\ = & \left(\frac{1}{2} \times A G \times G D\right)+\left(\frac{1}{2} \times B G \times G D\right)+\left(\frac{1}{2} \times B F \times E F\right)+\frac{1}{2} \times \\ & (E F+C H) \times F H+\left(\frac{1}{2} \times A H \times C H\right) \\ = & \left(\frac{1}{2} \times 200 \times x\right)+\left(\frac{1}{2} \times 200 \times x\right)+\left(\frac{1}{2} \times 100 \times 100\right) \\ & +\left\{\frac{1}{2} \times(100+50) \times 200\right\}+\left(\frac{1}{2} \times 100 \times 50\right) \end{aligned}$$ $$\begin{aligned} & =(100 x+100 x+5000+15000+2500) \mathrm{m}^{2} \\ & =(22500+200 x) \mathrm{m}^{2} . \\ & \therefore \quad 22500+200 x=27500 \Rightarrow 200 x=5000 \Rightarrow x=25 \mathrm{m} . \end{aligned}$$