Question

The height of a triangle is 6 m more than twice the length of the base. The area of the triangle is 18 m2. Find the height of the triangle.

Answer 1

Height is 12 meters

Explanation:

The area of a triangle is given by the formula:

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

Where

A is Area

b is base length

h is height

We are given "height is 6 MORE THAN twice the base", we can write this as:

h = 2b + 6

And, since it is given area is 18, we can put this into formula as:

`A=(1)/(2)bh\\18=(1)/(2)bh`

Now we put the equation of height [ h = 2b + 6 ] into this and solve for b first:

`18=(1)/(2)bh\\18=(1)/(2)b(2b+6)\\36=2b^2+6b\\2b^2+6b-36=0\\b^2+3b-18=0\\(b+6)(b-3)=0\\b = -6, 3`

Length can't be negative, so base = 3

We know h = 2b + 6, thus

h = 2(3) + 6 = 12

height is 12