SOLUTION: A right angled triangle has a height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1 centimeters. Find and expression for the base of the triangle.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A right angled triangle has a height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1 centimeters. Find and expression for the base of the triangle.       Log On


   

Question 681763: A right angled triangle has a height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1 centimeters. Find and expression for the base of the triangle.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1
Pythagoras theorem
hypotenuse^2= base^2+height^2
base^2= hypotenuse^2-height^2
=(4x-1)^2-(2x+3)^2
=16x^2-8x+1-(4x^2+12x+9)
=16x^2-8x+1-4x^2-12x-9
=12x^2-20x-8
=4(3x^2-5x-2)
=4(3x^2-6x+x-2)
=4(3x(x-2)+1(x-2))
=4(3x+1)(x-2)
base = 2sqrt%28%283x%2B1%29%28x-2%29%29cm