Question

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?.

Answer 1

`\huge{\boxed{\text{The height of the triangle is 6cm.}}}`

Explanation:

This question requires us to use a system of equations.

The area of a triangle is (1/2) * (base) * (height).

Thus, if b = base, and h = height

`(1)/(2) bh=36`

Additionally, from the problem, we know:

`b=h+6`

Then, via substitution, we can get

`(1)/(2) *(h+6)*h=36`

Then, simplify:

`(1)/(2) h^2+3h=36`

`(1)/(2) h^2+3h-36=0`

`((1)/(2) h-3)(h+12)=0`

Thus, the height must equal either 6 or -12, and because height cannot intrinsically be negative, the height must be 6.

Hope it helps :) and let me know if you want me to elaborate.