What is the base of the triangle in inches?

Question

The base of a triangle is 4 inches less than twice its height. If the area of the triangle is 360 square inches, what is the base of the triangle in inches? 

Answer 1

The formula for area of a triangle is

 

     A = ½bh     where b represents value of base and h represents value of height

 

in this problem let h = height and 2h - 4 = base

 

so A = ½(2h-4)(h) = 360      distribute the ½

 

              (h - 2)(h) = 360     distribute the h

 

                  h² - 2h = 360     subtract 360 from both sides

 

          h² - 2h - 360 = 0      factor the quadratic  360 = 36(10) or 18(20)  we use the 18(20) because the difference is -2

 

       (h - 20)(h + 18) = 0       set each factor equal to zero and solve each

 

h - 20 = 0         h + 18 = 0

 

      h = 20            h = -18

 

Since the  height can not be negative so we discard the -18 answer.  The only answer for height would be 20

 

When height = 20 then base = 2(20) - 4 = 40 - 4 = 36

 

CHECK

 

base = 36 and height = 20

 

A = ½bh

 

360 = ½(36)(20)

 

360 = (18)(20)

 

360 = 360√