Question

If a small rectangle represents the original size of a parking lot. And then its length and width were each extended by $w$ feet to make the larger rectangular. If the area of the enlarged lot is twice the area of the original lot, what is the value of $w$ ?

• A. $25$
• B. $50$
• C. $75$
• D. $100$
• E. $200$

Answer 1

The correct option is B $50$

Let the length and breadth of original lot be $150$ and $100$

Lenth and breadth of enlarged lot is $(150+w)and$(100+w)$

According to question

Area of enlarged lot $=2.$(Area of original lot)

$\to (150+w)(100+w)=2\times 100\times 150$

$\to 15000+250w+w^2=30000$

$\to w^2+250w-15000=0$

On solving we get

$w=50$ or $-300$

Neglecting negative term

we get $w=50$