Question

The rectangular fence is enclosed with an area $16$cm${}^2$. The width of the field is $6$ cm longer than the length of the fields. What are the dimensions of the field?

• A. length $=2$ cm, width $=6$ cm
• B. length $=1$ cm, width $=8$ cm
• C. length $=2$ cm, width $=8$ cm
• D. length $=3$ cm, width $=8$ cm

Answer 1

The correct option is C length $=2$ cm, width $=8$ cm

Let $x$ be the length of the field, then width of the field $=x+6$
Area of rectangle $=$ length $\times$ breadth
$16=x(x+6)$
$x^2+6x-16=0$
On factoring, we get,
$(x-2)(x+8)=0$
$x=2$ or $-8$
Neglect the negative answer as the length can't be negative, take $x=2$.
So, the length of the field is $2$ cm.
Then the width is $8$ cm.