solve using any method

Question

The area of a triangle is 54 inches²  If the height is 3 inches less than the base, find the length of the base and the height. Note that the area of a triangle is A=1/2bh

Answer 1

The area, A, of a triangle is:

 

A = (1/2)bh

 

where b = the base and h = the height.  The height is 3 inches less than the base, so h = b-3.  Substituting:

 

A = (1/2)bh

A = (1/2)b(b-3) = (1/2)(b² - 3b)

 

The area is given as 54 in²:

 

54 = (1/2)(b² - 3b)

108 = b² - 3b

0 = b² - 3b - 108

0 = (b-12)(b+9)

 

b = 12 and -9

 

Since you can't have a base with a negative length, b = 12 in.  h = b-3 = 9 in.