Question

A carpet of size $5m\times 2m$ has $25cm$ wide red border. The inner part of the carpet is blue in colour. Find the area of blue portion. What is the ratio of the areas of red portion to blue portion.

Answer 1

Given, size of carpet$=5\times 2m^2$ and width of border$=25$cm$=\frac{25}{100}=0.25$m

$\therefore$ Area of carpet $ABCD=AB\times BC=5\times 2=10m^2$ because area of rectangle$=$ length $\times$ breadth.

So, length of inner blue portion,$EF=AB-(2\times 0.25cm)=5-0.50=4.5$m

and breadth of inner blue portion $FG=BC-(2\times 0.25)=2-0.50=1.5$m

Area of blue portion$=$Area of rectangle$EFGK=EF\times FG=4.5\times 1.5=6.75m^2$

Now, area of red porion$=$Area of $ABCD-$Area of $EFGH=10-6.75=3.25m^2$

$\therefore$ Ratio of areas of red portion to blue portion$=3.25:6.75=13:27$