Question

A gardener has a cultivated plot that measures $4$ feet by $6$ feet. Next year, she wants to double the area of her plot by increasing the length and width by $x$ feet. Calculate the value of $x$.

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

$2$

Area of the current plot $=$ $4\times 6=24$square feet

Next year area of the new plot will be $=24\times 2=48$ Square feet.

She wants to increase the length and width by $x$ feet to get the area $48$

$\therefore (x+4)(x+6)=48$

$\Rightarrow x^2+10x+24=48$

$\Rightarrow x^2+10x-24=0$

$\Rightarrow x^2+12x-2x=24=0$

$\Rightarrow x(x+12)-2(x+12)=0$

$\Rightarrow x=-12,2$

Length and width never be negative so $x=2$ feet.