Subject: General Aptitude · Chapter: Area · Exam: 2005 · Marks: · Difficulty:
The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 5 cm and the breadth is less by 3 cm. Find the perimeter of the rectangle.
(a)17 cm
(b)26 cm
(c)30 cm
(d)34 cm
Answer
Answer (as printed): D
Explanation
Let the length of each side of the square be $x \mathrm{cm}$. Then, length of rectangle $=(x+5) \mathrm{cm}$ and its breadth = $(x-3) \mathrm{cm}$. $$\begin{aligned} & \therefore(x+5)(x-3)=x^{2} \Leftrightarrow x^{2}+2 x-15=x^{2} \Leftrightarrow x=\frac{15}{2} . \\ & \therefore \text { Length }=\left(\frac{15}{2}+5\right) \mathrm{cm}=\frac{25}{2} \mathrm{cm}, \text { breadth } \\ & \quad=\left(\frac{15}{2}-3\right) \mathrm{cm}=\frac{9}{2} \mathrm{cm} . \end{aligned}$$ Hence, perimeter $=2(l+b)=2\left(\frac{25}{2}+\frac{9}{2}\right) \mathrm{cm}=34 \mathrm{cm}$