9514 1404 393
Answer:
I, III
Step-by-step explanation:
You know from your study of the Pythagorean theorem that a triangle with sides 3, 4, and 5 will be a right triangle. Any scaled version of this triangle will also be a right triangle, so it is helpful to learn to recognize when scaled values of these numbers are used.
I -- the scale factor for a 3-4-5 right triangle is 2/10
II -- no isosceles right triangle has integer side lengths. (not a right triangle)
III -- the scale factor for a 3-4-5 right triangle is 1/13
IV -- the lengths do not form a triangle
Triangles I and III are right triangles.
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<em>Additional comment</em>
The sides of an isosceles right triangle have the ratios 1 : 1 : √2. The square root of 2 is irrational. No scaled version of this triangle can have rational side lengths.
