Mensuration Ques 6
Question
The area of a rectangular park is 1050 sq.m. and its perimeter is 130 metre. There is a $2.5 m$ wide path inside the park all around. The cost of construction of path is ₹ 40 per sq. metre. Find the total cost of construction of whole path.
(1) ₹ 10000
(2) ₹ 12000
(3) ₹ 12500
(4) ₹ 8500
(5) None of these
(Bank of Baroda PO Exam. 14.08.2014)
Show Answer
Correct Answer: (2)
Solution: (2)
Length of rectangular park $=$ $x$ metre
Breadth $=y$ metre
$\therefore x y=1050$ and $2(x+y)=130$
$\Rightarrow x+y=\frac{130}{2}=65$
$\therefore(x-y)^{2}=(x+y)^{2}-4 x y$
$=(65)^{2}-4 \times 1050$ $=4225-4200=25$
$\therefore x-y=\sqrt{25}=5$
$\therefore$ By adding equations (ii) and (iii),
$2 x=70 $
$\Rightarrow x=35$ metre
From equation (ii),
$y=65-x=65-35=30$ metre
Length excluding path $=35-5=30$ metre
Breadth $=30-5=25$ metre
$\therefore$ Area of path $=1050-30 \times 25$ $=1050-750=300$ sq. metre
$\therefore$ Total cost $=300 \times 40$ $= \text{₹} 12000$
BETA
