Mensuration Ques 23
Question
The perimeter of a rectangle is $x$ units and the circumference of a circle is 8 units more than the perimeter of the rectangle. The ratio of radius of circle and length of the rectangle is $1: 2$ and the ratio of length and breadth of rectangle is $7: 3$. Find the length of the rectangle?
(1) 14
(2) 21
(3) 28
(4) 35
(5) 7
(IBPS Bank PO/MT CWE-VI (Pre Exam), 16.10.2016 (Second Sitting))
Show Answer
Correct Answer: (3)
Solution: (3)
Length of rectangle $=2 y$ units
Radius of circle $=y$ units
Breadth of rectangle $=\frac{3}{7} \times 2 y=\frac{6 y}{7}$ units
$\therefore$ Perimeter of rectangle $=2\left(2 y+\frac{6 y}{7}\right)$
$=2\left(\frac{14 y+6 y}{7}\right)$ $=\frac{40 y}{7}$ units
According to the question,
$\therefore 2 \pi y=\frac{40 y}{7}+8$
$\Rightarrow \frac{2 \times 22}{7} y-\frac{40 y}{7}=8$
$\Rightarrow \frac{4 y}{7}=8 $
$\Rightarrow y=\frac{8 \times 7}{4}=14$
$\therefore$ Length of rectangle $=2 \times 14$ $=28$ units
BETA
