A simple triangle problem

Someone sent in this very simple question (a student?).
Leg b of the right triangle is twice as long as the base a.
If the area is 36 cm squared, what is the length in of the leg b?

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:
right triangle

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

a2 = 36

a = 6.

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


Anonymous said…
Does 'leg' in a right triangle only mean one of the perpendicular sides? If not, then the hypotenuse can also be twice of a leg.
Maria Miller said…
Yep. The legs are the other two sides of a right triangle, but not the hypotenuse.

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