Answer
The dimensions of the parcel are $120$ ft in length and $50$ ft in width.
Work Step by Step
As we can see in the picture, there is a right triangle. So, we can use the Pythagorean Theorem $a^2+b^2=c^2$ to find $x$.
$(x+70)^2+x^2=130^2$
$(x^2+70x+70x+4900)+x^2=16900$
$2x^2+140x+4900-16900=0$
$2x^2+140x-12000=0$
We can factor out a $2$ and then we can use the quadratic formula
$2(x^2+70x-6000)=0$
$x^2+70x-6000=0$
$x={-70\pm\sqrt{(-70)^2-4(1)(-6000)}\over 2(1)}$
$x={-70\pm\sqrt{4900+24000}\over 2}$
$x={-70\pm\sqrt{28900}\over 2}$
We're only going to calculate the positive square root since negative values aren't used to measure distance.
$x= {-70+170\over2}= {100\over 2}=50$
Therefore, the dimensions of the parcel are $70+50 = 120$ ft in length and $50$ ft in width
