### A simple triangle problem

Someone sent in this very simple question (a student?).

A little bit of algebra helps in this problem.

FIRST strive to make a picture. Need a right triangle, the leg twice as long as the base. Here in my picture things aren't exactly to the scale, but it suffices for illustration purposes:

So we actually know that b = 2a.

The area of a triangle here is base times height over 2, and remember the height is the other leg, and it's twice the base:

area = ba/2 = (2a)(a)/2 , and this is 36 (given).

So we get our equation:

(2a)(a)/2 = 36

a

a = 6.

The leg b is therefore 12 cm long. check: Legs are 12 and 6, so the area is 12 * 6 / 2 = 36.

Legbof the right triangle is twice as long as the basea.

If the area is 36 cm squared, what is the length in of the legb?

A little bit of algebra helps in this problem.

FIRST strive to make a picture. Need a right triangle, the leg twice as long as the base. Here in my picture things aren't exactly to the scale, but it suffices for illustration purposes:

So we actually know that b = 2a.

The area of a triangle here is base times height over 2, and remember the height is the other leg, and it's twice the base:

area = ba/2 = (2a)(a)/2 , and this is 36 (given).

So we get our equation:

(2a)(a)/2 = 36

a

^{2}= 36a = 6.

The leg b is therefore 12 cm long. check: Legs are 12 and 6, so the area is 12 * 6 / 2 = 36.