The area of a triangle is 54 square cm. Find the height of the triangle if the height is 6 cm less than 4 times the length of the base.

Question

Algebra word problem has to be factored out to find the x's

Answer 1

Let b = the length of the base of the triangle and h = its height.  The height is given as 6 cm less than 4 times the base, or h = 4b-6.  The triangle's area is:

 

Area = (1/2)bh

 

54 = (1/2)(b)(4b-6)

54 = 2b² - 3b

0 = 2b² - 3b - 54

 

Factors to:

 

0 = (2b+9)(b-6)

 

b = -9/2 and 6

 

Since we can't have a negative length, b = 6.

 

h = 4b - 6 = 4(6) - 6 = 18 cm

 

Check:

Area = (1/2)bh

54 = (1/2)(6)(18)

54 = 54

Check!!!

Answer 2

A=(1/2)(b)(h)

54=(1/2)(b)(4b-6)

54=2b²-3b

2b²-3b-54=0

2*54=2*2*3*3*3=(2*2*3)*(3*3) and 9-12=-3, the coefficient of the middle term

factor

(2b+9)(b-6)=0

b-6=0

b=6 cm

54=(1/2)(6)(h)

54=3h

h=54/3

h=18 cm for the height