Question 1193675
<br>
The base, altitude, and diagonal form a right triangle with legs x+11 and x+7 and hypotenuse 4x.  Use the Pythagorean Theorem to find x and answer the questions.<br>
{{{(x+11)^2+(x+7)^2=(4x)^2}}}
{{{x^2+22x+121+x^2+14x+49=16x^2}}}
{{{2x^2+36x+170=16x^2}}}
{{{14x^2-36x-170=0}}}
{{{7x^2-18x-85=0}}}
{{{(x-5)(7x+17)=0}}}<br>
x = 5 or x=-17/7<br>
Obviously the negative answer makes no sense in the problem, so x=5.<br>
ANSWERS:
base = x+11 = 16
altitude = x+7=12
diagonal = 4x = 20<br>