Question

A triangle has side lengths of 20 cm 27 cm and 21 cm. Is the triangle a right triangle? SHOW YOUR WORK TO PRO

VE IT!

Answer 1

When a triangle is a right triangle, Pythagorean theorem must work on it.
The Pythagorean theorem states: a^2+b^2=c^2
20^2+21^2=27^2
400+441=729
841=729
false

Therefore, the triangle is not a right triangle

Answer 2

We have a triangle with sides a = 20 cm, b = 27 cm and c = 21 cm.

In a right triangle, according to the Pythagorean theorem, the square of the longest side (hypotenuse) is equal to the sum of squares of the other two sides. In our case, as 27 cm is the longest side, it would serve as the hypotenuse if the triangle is a right triangle.

So, we would check if
b² = a² + c²
or
27² = 20² + 21².

Calculating, we get:
729 = 400 + 441
729 = 841

From the above calculations it's clear that the equation is incorrect, meaning the square of the length of side 'b' is not equal to the sum of squares of the lengths of sides 'a' and 'c'. This tells us that the triangle is not a right triangle.

Therefore, we can conclude that the given triangle, with sides 20 cm, 21 cm, and 27 cm, is not a right triangle.