SOLUTION: a square with side length a, and a triangle whose base and height both have length b, have the same area. Write an equation for b in terms of a

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: a square with side length a, and a triangle whose base and height both have length b, have the same area. Write an equation for b in terms of a      Log On


   

Question 595234: a square with side length a, and a triangle whose base and height both have length b, have the same area. Write an equation for b in terms of a
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Area of square: A+=+a%5E2

Area of triangle A+=+%28b%5E2%29%2F2


Since the two areas are equal, this means %28b%5E2%29%2F2=a%5E2


Solve for 'b' to get b+=+sqrt%282a%5E2%29 which simplifies to b+=+a%2Asqrt%282%29