Right Triangle Question

[JaimieG385]

Hi,

If it's given that the hypotenuse of a right triangle is 5, is this sufficient to assume that the triangle is a 3-4-5 triangle? Is it possible for the lengths of the legs of the triangle to be something other than 3 or 4 in this situation?

[RahulS31]

Well, in this case you may assume it as an 3-4-5 right triangle (Pythagorean triplet in its simplest form). But always be careful while assuming on geometry based problems. (better if your assumptions are derived logically)

Let's say you see a hypotenuse of 50, you might think the triangle is a scaled up version of 3-4-5 (30-40-50). It could also be 7-24-25 (14-48-50).

[RonPurewal]

Hi,

If it's given that the hypotenuse of a right triangle is 5, is this sufficient to assume that the triangle is a 3-4-5 triangle? Is it possible for the lengths of the legs of the triangle to be something other than 3 or 4 in this situation?

they could be lots and lots of other things.

3, 4, 5
√12.5, √12.5, 5
1, √24 (= 2√6), 5

basically, √(whatever), √(25 - whatever), and 5.

[RonPurewal]

also, you can just draw the situation (or just think about what it looks like).

• you know that there are lots and lots of different shapes that a right triangle can have.

• you can draw ANY of those shapes with a hypotenuse of 5 units. (in fact, you can draw any of them with a hypotenuse of any length-- just scale up or down accordingly.)

so, it should be clear that there are lots of possibilities, even if you have trouble coming up with precise numerical values.