Which set of measurements could be the side lengths of a right triangle? 32 cm, 21 cm, 24 cm 33 cm, 18 cm, 30 cm 30 cm, 19 cm, 27 cm 30 cm, 18 cm, 24 cm

Question

 

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Answer 1

The Pythagorean Theorem applies to all right triangles:      c² = a² + b²

 

So, if the sum of the squares of two numbers equals the square of the third number, it is a right triangle.

 

For easy math, put a, b, c in ascending order (since the hypotenuse is always the longest side):

 

   a        b       c             a²              b²                c²             a²+b²       Right Triangle?

 

  21      24     32          441          576              1024            1017                No

 

  18      30     33          324          900              1089            1224                No

 

  19      27     30          361          729                900            1090                No

 

  18      24     30     You fill in. ...

 

Answer 2

Think about some of the common right triangles that we encounter. One is the 3-4-5 triangle with legs of length 3 and 4 units, and a hypotenuse of length 5. Consider 18, 24, and 30. These are multiples of 3, 4, and 5, respectively. 

3 * 6 = 18

4 * 6 = 24

5 * 6 = 30

 

As you can see, there is a common factor of 6. In fact, a right triangle with lengths 18-24-30 is similar to the 3-4-5 right triangle with which we are familiar.