Question

A carpenter had a board which measured $3m\times 2m$. She cut out a rectangular piece of $250cm\times 90cm$. What is the ratio of the area of a cut-out piece and the remaining piece?

Answer 1

Given, board measure = $3m\times 2m$
Area of board = Length $\times$ Breadth
$=3\times 2=6m^2$
She cut out a rectangular piece $=250cm\times 90cm$
Area of the piece $=250\times 90c{m}^2$
= $22500c{m}^2$
= $\frac{22500}{10000}{m}^2[\because 1m^2=10000c{m}^2]$
= $2.25m^2$
Remaining area of board = $(6-2.25)m^2=3.75m^2$
Ratio of the area of cut out piece to the remaining piece

= $\frac{\text{Area of cut out piece}}{\text{Area of remaining piece}}$

= $\frac{2.25m^2}{3.75m^2}$
= $\frac{225}{375}=\frac{3}{5}$ = $3:5$

Hence, the ratio of the area of a cut-out piece and the remaining piece 3 : 5.