Hi Bailey.

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

Let b = the base length, h = the height, and A = the area. Then

A = (1/2) b h.

You said "the length of the base...is 1cm less than 5 times the height...". So:

b = 5h - 1.

Therefore you can substitute this expression for b into the area equation. Thus A = (1/2) b h becomes:

A = (1/2) (5h - 1) h.

You said "the area...is 21 square cm". So A = 21.

21 = (1/2) (5h - 1) h.

This is a quadratic equation. When we put it in standard form we get:

0 = 5h² - h - 42

Now can you solve for the height (h) using factoring or completion of the square? Remember that the height of a triangle must be a positive number. Then you can use that to find b using b = 5h - 1.

Write us back if you are still stuck (tell us where you have trouble).

Cheers,
Stephen La Rocque