The area of a triangle is 36 cm2. The height of the triangle is 6 cm less than the base. What is the height of the triangle?
A) 4 cm
B) 6 cm
C) 8 cm
D) 12 cm

Height of triangle = 6 cm

Step-by-step explanation:

Let,

Height of triangle = h

Base of triangle = b

Given Data:

Area of  triangle = A =

According to given condition:

h = b - 6

To find out:  

Height of triangle = h = ?  

Formula:  

Area of  triangle = A = (b × h)/2

Solution:  

Area of  triangle = A = (b × h)/2

36 = (b × h)/2

36 × 2 = b × (b - 6 )         ∴h = b - 6

b- 12 = 0       or    b + 6 = 0

b = 12           or    b = -6

As base value is always positive, so

Base of triangle = b = 12 cm

h = b - 6

h = 12 - 6

Height of triangle = 6 cm