Question

A border of uniform width is placed around a rectangular photograph that measures $8$ inches by $10$ inches. If the area of the border is $144$ square inches, what is the width of the border, in inches?

• A. $3$
• B. $4$
• C. $6$
• D. $8$
• E. $9$

Answer 1

The correct option is A $3$

Let the width of the border be ${}^{\prime }{x}^{\prime }$ inch.

Therefore area of shaded region $=$ $(10+2x)(8+2x)-10\times 8$

$\Rightarrow 144=80+20x+16x+{4x}^2-80$

$\Rightarrow {4x}^2+36x-144=0\Rightarrow x^2+9x-36=0$

$\Rightarrow x^2+12x-3x-36=0\Rightarrow (x+12)(x-3)=0$

$\therefore x=-12,$, $3$ (neglecting negative value.)

$\therefore$ Therefore width of border is $3$ inches.