The height of a triangle is 2 inches less than the base. if the area is 60 square inches, find the base.

base = 12  inches

Height = = 10  inches

Step-by-step explanation:

Given  

Area of triangle = 60 sq inches  

Let the base =x  

Height will be= x-2

Area of triangle = 1/2 base × height

                       60  =1/2   (x)(x-2)equation 1  

                       60 x 2 =  x²-2x

                      120= x²-2x

x²-2x-120 = 0

by factorization method  

x²-12x+10x-120=0

x(x-12)+10(x-12)=0

(x+10)(x-12)=0

X+10 = 0                          x-12=0

X=-10                                x=12

So either x = -10 or x =12

Checking  

Considering positive x = 12

Area = 1/2  (x)(x-2)=  ½ (12)(12-2)

  60     =1/2 x 120

60 = 60 ……. Satisfied, so it means the value of x i.e. base will be= 12  inches

Height = x-2 =12-2= 10  inches