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 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