The base of a triangle is twice that of its height. If the area is 36 square centimeters, then find the length of its base and height.

height = 6 cm

base = 12 cm

Step-by-step explanation:

Let the base of the triangle is denoted by b

Let the height of the triangle is denoted by h

We are given that base of a triangle is twice that of its height,

b = 2h

Recall that area of a triangle is given by,

A = ½*b*h

We are given that area of the triangle is 36 cm²

36 = ½*b*h

Substitute b = 2h in the above equation

36 = ½*2h*h

36 = h*h

h² = 36

h = √36

h = 6 cm

Therefore, the height of the triangle is 6 cm

b = 2h

b = 2 (6)

b = 12 cm

Therefore, the base of the triangle is 12 cm

Verification:

A = ½*b*h

A = ½*12*6

A = ½*72

A = 36 cm²

Hence proved