Can the legs in a right triangle ever be longer than the hypotenuse? Why or why not?

Question

Can the legs in a right triangle ever be longer than the hypotenuse? Why or why not?

Answer 1

No, a property of right triangles is that they all satisfy the Pythagorean Theorem a^2 +b^2 = c^2.

where C is the hypotenuse.

so upon inspection we can see that all these numbers must be positive, since they are being squared.

therefore it is impossible for a or b to be larger than c.

Answer 2

hypotenuse

[hīˈpätnˌ(y)o͞os]

NOUN

1. the longest side of a right triangle, opposite the right angle.

Answer 3

No, it can't. The largest angle in a right triangle is 90 degrees and it is the largest angle of the triangle. The side opposite the largest angle has to be the largest side.