Question 366044
The length of the base of a triangle is 6 feet more than the length of the altitude.
 The area of the triangle is 18 square feet.
 Find the length of the base and of the altitude to the base.
:
Area of a triangle:  .5*b*a = 18
Given that: b = (a+6)
therefore:
.5*(a+6)*a = 18
multiply both sides by 2 to get rid of the .5
a(a+6) = 36
a^2 + 6a - 36 = 0; a quadratic equation
Use the quadratic formula to find a:
{{{a = (-6 +- sqrt(6^2-4*1*-36 ))/(2*1) }}}
Do the math here, should get a positive solution; a ~ 3.71 ft is the altitude
then, 9.71 ft is the base
:
:
Check: .5*9.71*3.71 ~ 18 sq/ft