Answer
The width is $25 ft$ and the length is $35 ft$.
Work Step by Step
$\underline{\textbf{Givens: }}$
$Area = 875 ft^2$
$Width = W $
$Length (L)= W+ 10ft$
We know Area of a Rectangle $= L \times W$
i.e
$x(x+10)=875$
$\Rightarrow x(x+10)=875$
$\Rightarrow x^2+10x=875$
$\Rightarrow x^2+10x-875=0$
the quadratic formula, where $a=1, b=10$ and $c=-875$
$\Rightarrow x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(10)\pm\sqrt{(10)^2-4(1)(-875)}}{2(1)}$
$\Rightarrow x=\dfrac{-10\pm\sqrt{100+3500}}{2}=\dfrac{-10\pm\sqrt{3600}}{2}$
$\Rightarrow x=\dfrac{-10\pm60}{2}$
$\Rightarrow x=\dfrac{-10+60}{2}=\dfrac{50}{2}=25$
or $x=\dfrac{-10-60}{2}=\dfrac{-70}{2}=-35$ $\color{red}{(Rejected)} $
i.e $x=25$
Therefore, the width is $25 ft$ and the length is $35 ft$.
