SOLUTION: The length of the base of a triangle is 6 feet more than the length of the altitude of the base. The area of the triangle is 18 square feet. Find the lenght of the base and of the

Algebra ->  Triangles -> SOLUTION: The length of the base of a triangle is 6 feet more than the length of the altitude of the base. The area of the triangle is 18 square feet. Find the lenght of the base and of the       Log On


   

Question 366044: The length of the base of a triangle is 6 feet more than the length of the altitude of the base. The area of the triangle is 18 square feet. Find the lenght of the base and of the altitude to the base.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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+=+%28-6+%2B-+sqrt%286%5E2-4%2A1%2A-36+%29%29%2F%282%2A1%29+
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