A triangle with area 91 square inches has a height that is two less than four times the base. Find the base and height of the triangle (in inches).

Answer 1

Hi Tiffany!

For this question, we need to know the area formula for a triangle: that would be A = 0.5bh

While we don't know the base and height of the triangle yet, we do know that the height is two less than four times the base. Let's try to convert that sentence into an equation. "is" almost always means "equals", "less" tells us we're subtracting, and "times" means multiplication. Putting all that together, we get: h = 4b - 2

Now we can subsitute into the area formula.

A = 0.5b(4b - 2)

But since we know the area is 91 square inches, we can say:

91 = 0.5b(4b - 2)

At this point, we solve the equation with some algebraic manipulation. You should get two values: one positive and one negative. Which one do we want to use here? Remember that b represents the length of the base.

Once we figure that out, we can then take that value of b and plug it back into any equation that relates b and h, then solve for h. And that should give us b and h!

Hope this helps!