Question

A drawing of a portion of a wall that is to be covered with wallpaper is given below. If the wallpaper is sold in rolls that are $0.5$ ft wide and $30$ ft long, how many such rolls will be needed to cover the wall?

• A. $12$
• B. $18$
• C. $16$
• D. $15$

Answer 1

The correct option is A $12$



Overall area of the wall $=$ Area of $\Delta ADC+$Area of $ADEB+$ Area of $BEF$
In $\Delta ADC$,
Base, $b=5$ ft, height, $h=12$ ft
Area of $\Delta ADC=\frac{1}{2}\times 5\times 12=5times6=30f{t}^2$

BEF has the same dimensions as $\Delta ADC$,
Area of$\Delta BEF=$ Area of $\Delta ADC=30f{t}^2$

In rectangle $ABDE$,
$Length,l=10ft$
$width,w=12ft$
Area of $ADEB=l\times w=10\times 12=120f{t}^2$
Overall area $=30+30+120=60+120=180f{t}^2$
Thus, wallpaper of an area of $180f{t}^2$ is needed to cover the wall.

Area of each roll of wallpaper $=0.5\times 30=15f{t}^2$

Number of rolls $=\frac{Totalareaofwall}{Areaofeachroll}=\frac{180}{15}=12$

Thus, $12$ rolls will be needed to cover the wall.