Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The perimeter of a rectangle and a square are 160 m each. The area of the rectangle is less than that of the square by 100 sq. m. The length of the rectangle is
(a)30 m
(b)40 m
(c)50 m
(d)60 m
Answer
Answer (as printed): A
Explanation
Perimeter of square $=160 \mathrm{m}$. Side of square $=\left(\frac{160}{4}\right) \mathrm{m}=40 \mathrm{m}$. Area of square $=(40 \times 40) \mathrm{m}^{2}=1600 \mathrm{m}^{2}$ Area of rectangle $=(1600-100) \mathrm{m}^{2}=1500 \mathrm{m}^{2}$. Let the length and breadth of the rectangle be $l$ and $b$ respectively. Then, $2(l+b)=160 \Rightarrow l+b=80 \Rightarrow b=80-l$. $$\begin{aligned} \therefore l b=1500 & \Rightarrow l(80-l)=1500 \Rightarrow 80 l-l^{2}=1500 \\ & \Rightarrow l^{2}-80 l+1500=0 \Rightarrow(l-50)(l-30)=0 \\ & \Rightarrow l=50 . \end{aligned}$$