Question

Mark has a rectangular plot of land of length $730$ feet and width $600$ feet. He wants to make a house on the biggest square area of the plot possible and a garden on the remaining land.
What will the area of the garden be?

• A. $438,000\text{sq ft}$
• B. $36,000\text{sq ft}$
• C. $360,000\text{sq ft}$
• D. $78,000\text{sq ft}$

Answer 1

The correct option is D $78,000\text{sq ft}$

Mark wants to make a house on the biggest square area of the plot possible. For a square area, the length and the width of the plot should be equal.
Here, length of the rectangular plot $=730\text{ft}$
Width of the rectangular plot $=600\text{ft}$
The dimensions of the biggest possible square area are $600\text{ft}$ by $600\text{ft}$.
Area of the plot for the house $=l\times l$
$=600\times 600$
$=360,000\text{sq ft}$
Length of the plot for the garden $=730-600=130\text{ft}$
Width of the plot for the garden $=600\text{ft}$
Area of the plot for the garden $=l\times w$
$=130\times 600$
$=78,000\text{sq ft}$

Therefore, the area of the plot for the garden will be $78,000\text{sq ft}$