The base of a triangle is 10 inches more than 3 times the height. if the area of the triangle is 16 square inches, find the base and the height

So for this you will be making an equation based on the info given and the formula

Let x = height

Our equation will be

Firstly, you want to multiply everything on the left side to get

Next, subtract 16 on each side to get

Next, we will be completing the square. And to do that, find the factors that both multiply to -24 (1.5(-16)) and add up to 5. In this case, that will be 8 and -3. With this info, replace 5x and put in 8x and -3x.

Next, you will be factoring 1.5x^2-3x and 8x-16 separately. Make sure that they end up with the same number inside the parentheses.

With this, rewrite the equation as . We have now completed the square. Now to find x, we will need to set 1.5x+8 and x-2 to zero.

Since the length can't be negative, the length is 2 in. To find the base, just plug in 2 in the x variable of 3x+10.

In short, the height is 2 in and the base is 16 in.

9x