Question

Tabitha says she can find the length of both legs of an isosceles right triangle if she knows the length of the hypotenuse. Amanda says it can’t be done. Who’s correct? Explain

Answer 1

Amanda is correct. In an isosceles right triangle, the two legs are congruent, meaning they have the same length. However, knowing only the size of the hypotenuse does not uniquely determine the lengths of the legs.

Step-by-step explanation:

Consider the Pythagorean theorem, which relates the lengths of the sides of a right triangle:c2=a2+b2c2=a2+b2where cc is the length of the hypotenuse, and aa and bb are the lengths of the legs.In an isosceles right triangle, a=ba=b. If you know cc, you have one equation with two unknowns (aa and bb). Without additional information, you cannot uniquely determine the values of aa and bb. Therefore, Tabitha's claim is incorrect. Knowing the length of the hypotenuse alone is not sufficient to find the lengths of both legs in an isosceles right triangle.