Question

Two sides of a right triangle are equal to 3m and 4m. Find the length of the third side. (Two cases)

Answer 1

We will use the Pythagorean Theorem to solve both cases.   
Case 1: Given sides are both legs of the triangle:  
3^2 + 4^2 = c^2 
9 + 16 = 25 = c^2
 c = 5  
Case 2: Given sides are one leg and the hypotenuse:
 a^2 + 3^2 = 4^2
 a^2 = 4^2 - 3^2 = 16 - 9 = 7
 a^2 = 7^(1/2)  
 The third side of the given right triangle could be five or the square root of seven.