The distances between three cities
are 77 miles, 36 miles, and 49 miles. Do the positions of these cities
form a right triangle?
We can answer this question by
considering the Pythagorean theorem. This states that 𝑎 squared plus 𝑏
squared is equal to 𝑐 squared, where 𝑐 is the longest side or hypotenuse of a
right triangle. The converse of the Pythagorean
theorem states that if the square of the longest side of a triangle is equal to the
sum of the squares of the other two sides, then the triangle is right angled.
In this question, we need to
consider the sum of the squares of 36 and 49 and see if they’re equal to the square
of 77. 77 squared is equal to 5929. 36 squared plus 49 squared is equal
to 3697. These two values are not equal. This means that 36 squared plus 49
squared is not equal to 77 squared. We can, therefore, conclude that as
the three distances do not satisfy the Pythagorean theorem, the triangle is not a