Question

4) Which of the following could represent the lengths of the sides of a right triangle? Hint: Remember Pythagorean Triple :a) 3,4,5b) 5,12,12c) 15,30,45d) 24,32,40

Answer 1

We have to find which of the following could represent the lengths of the sides of a right triangle.

To be a right triangle, the lengths a, b and c have to satisfy the Pithagorean theorem:

`a^2+b^2=c^2`

Of course, c has to be the largest of the sides.

We can write for the first option:

`\begin{gathered} 3^2+4^2=5^2 \\ 9+16=25 \\ 25=25 \end{gathered}`

As the expression is satisfied, we can conclude that the triangles with sides 3, 4 and 5 is a right triangle.

Option B (5,12,12) can not be a right triangle, as it has 2 largest sides. It can only have one, that is the hypothenuse. NOTE: it can have two equal smallest sides, but no two largest.

Option C is 15, 30 and 45. We test the equation: