Answer :
Answer:
width = 160 ft and length = 168 ft
Step-by-step explanation:
A parcel of land is 8 ft longer than it is wide.
diagonal is 232 ft long.
Let 'w' be the width of the parcel and w+8 is the length of the parcel
Diagonal is the hypotenuse . use Pythagorean theorem to find out width 'w'
[tex]c^2=a^2+b^2\\[/tex]
c=232 , a= w+8 and b= w
[tex]232^2= (w+8)^2+w^2[/tex]
[tex]53824=2w^2+16w+64+w^2[/tex]
[tex]53824=3w^2+16w+64[/tex]
Subtract 53824 from both sides
[tex]2w^2+16w-53760=0[/tex]
Apply quadratic formula
[tex]w=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]w=\frac{-16\pm \sqrt{16^2-4\cdot \:2\left(-53760\right)}}{2\cdot \:2}[/tex]
[tex]w=\frac{-16 + \sqrt{16^2-4\cdot \:2\left(-53760\right)}}{2\cdot \:2}=160[/tex]
[tex]w=\frac{-16 - \sqrt{16^2-4\cdot \:2\left(-53760\right)}}{2\cdot \:2}=-160[/tex]
width = 160 and length = 160+8= 168