Solving Quadratics using the Quadratic Equation

Question

The base of a triangle is twelve more than twice its height. If the area of the triangle is 49 square​ centimeters, find its base and height.

The height of the triangle is

and the base of the triangle is

Answer 1

b= 12+2h

area = 49 = bh/2

bh = 98

= (12+2h)h = 98

= 12h +2h^2 = 98

h^2 + 6h -49 = 0

h +6h + 9 = 49+9 =58

(h+3)^2 = 58

h+3 = sqr58

h = -3 + sqr58

h = about 4.616 cm = the triangle's height

b = 12+2(4.616) = 12+9.232 = 21.232 = triangle's base

check the answer, using 4.6 and 21 approximations

area = about 4.6(21)/2 = 2.3(21) = about 48.3 = about 49 given rounding approximations