Question

The length of the larger plot is twice the sum of the length and width of the smaller plot. The width of the larger plot is $3$ times the difference between the length and width of the smaller plot.

Which among the following expressions represents the area of the larger plot if the length and width of the smaller plot is $50$ feet and $p$ feet, respectively?

• A. $(100-2p)\times (150+3p)$
• B. $(100-2p)-(150+3p)$
• C. $(100+2p)+(150-3p)$
• D. $(100+2p)\times (150-3p)$

Answer 1

The correct option is D $(100+2p)\times (150-3p)$

Length of the smaller plot $=50$ ft
Width of the smaller plot $=p$ ft
Length of the larger plot $=$ twice the sum of the length and width of the smaller plot
$=2$ (sum of the length and width of the smaller plot)
$=2(50+p)$
Width of the larger plot $=3$ times the difference between the length and width of the smaller plot
$=3$(difference between the length and width of the plot)
$=3(50-p)$
Area of the larger plot $=$ length $\times$ width
$=[2$ (sum of the length and width of the smaller plot)$]\times [3$ (difference between length and width of the plot)]
$=2(50+p)\times 3(50-p)$
$=(2\times 50+2\times p)\times (3\times 50-3\times p)$
$=(100+2p)\times (150-3p)$