SOLUTION: The height of a triangle is 2 millimeters less than the base. If the area is 60 square millimeters, find the base.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The height of a triangle is 2 millimeters less than the base. If the area is 60 square millimeters, find the base.      Log On


   

Question 33680: The height of a triangle is 2 millimeters less than the base. If the area is 60 square millimeters, find the base.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a triangle:
A+=+%281%2F2%29bh Where: A = 60, h = b-2
60+=+%281%2F2%29b%28b-2%29 Simplify and solve for b.
60+=+%281%2F2%29%28b%5E2-2b%29 Multiply both sides by 2.
120+=+b%5E2-2b Subtract 120 from both sides of the equation.
b%5E2-2b-120+=+0 Solve this quadratic for b by factoring.
%28b%2B10%29%28b-12%29+=+0 Apply the zero products principle.
b%2B10+=+0 and/or b-12+=+0
If b%2B10+=+0 then b+=+-10 Discard this solution as b can only be a positive value.
If b-12+=+0 then b+=+12 This solution is acceptable.
The length of the base is 12 mm.
The height would be 10 mm
Check:
A+=+%281%2F2%29bh
A+=+%281%2F2%29%2812%29%2810%29
A+=+%281%2F2%29%28120%29
A+=+60 sq.mm.