# Mensuration Part 4

Problem 1: If the perimeter of a rectangle and a square are equal and the ratio of two adjacent sides of the rectangle is 1: 2 then the ratio of the area of the rectangle and that of the square is?

Solution:

Length =x , Breadth = y

If the perimeter of a rectangle and a square are equal
2(l+b) = 4a
2(x+2x) = 4a
3x=2a
$a=\frac{3}{2}x$
$2x^{2}:\frac{9}{4}x^{2}$
8  :  9
Problem 2: The cost of fencing a circular plot at the rate of Rs.15 per meter is Rs.3300. What will be the cost of flooring the plot at the rate of Rs.100 per square meter?
Solution:
RS. 15 —–> 1meter
RS. 3300—–>?$\frac{3300}{15}=220$m
Perimeter = 220
$2\Pi&space;r=220$
$r=220\times&space;\frac{7}{22}\times&space;\frac{1}{2}$
r=35
Area = $\Pi&space;r^{2}$
$\frac{22}{7}\times&space;35\times&space;35=3850&space;m^{2}$
1m——->RS.100
3850m—->? 3850*100 = 385000