how many different triangles,if any, can be drawn with one 90 degree angle and side lengths of 5 centimeters and 12 centimeters

Question

Answer choices

a)0

b) 1

c) 2

d) infinitely 

Answer 1

Only 1!

 

In 2 right triangles, if the legs are equal, each to each, the triangles are congruent.

 

This triangle, by the way, is the next to smallest right triangle with integer sides.  The smallest has sides 3, 4 & 5.

What is the hypotenuse of this triangle?

Answer 2

If leg lengths are 5 and 12 then the only such right triangle is the famous 5-12-13 Pythagoroean Triple.

 

If 12 is the hypotenuse and a leg has length 5, then there's another right triangle. Unknown leg length x would satisfy 12^2 = 5^2 + x^2.

 

IT LOOKS AS IF THERE ARE TWO possible such right triangles.  Sorry, Natalie, your Comment does not appear to be correct