Translate the given into a mathematical statement and write the equation in standard form

Question

The base of a triangle is one-half less than twice it's height x. The area of the triangle is 34.5 square units.

Answer 1

b = 2x - 1/2

A=bx/2 = 34.5

34.5 = (2x-1/2)x/2 = x^2 -x/4

x^2 -x/4 -34.5 = 0

x = (1/4)/2 +/- (1/2)sqr(1/4 +4(34.5))

x = 1/8 +/- about 5.88

x = 0.125 +5.88 = 6= triangle's height

b = 2(6)-1/2 = 11.5 = base

Area = 34.5 = bx/2 = 11.5(6)/2 = 11.5(3) = 34.5