Question

Using the Converse of the
Pythagorean Theorem,
explain whether a triangle with
sides 15, 10, and 12 is a right
triangle.
No, because 244 is not
equal to 225.
No, because 325 is not
equal to 144.
No, because 369 is not
equal to 100.
No, because 22 is not
equal to 15.

Answer 1

To determine whether a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we first need to identify the lengths of the sides.

In a triangle, let \( a = 10 \), \( b = 12 \), and \( c = 15 \) (where \( c \) is the longest side). According to the Converse of the Pythagorean Theorem, a triangle is a right triangle if the square of the longest side is equal to the sum of the squares of the other two sides.

Now we calculate:

1. Calculate \( c^2 \):
\[
c^2 = 15^2 = 225
\]

2. Calculate \( a^2 + b^2 \):
\[
a^2 + b^2 = 10^2 + 12^2 = 100 + 144 = 244
\]

Now we check if \( c^2 \) equals \( a^2 + b^2 \):

- We have \( 225 \) (which is \( c^2 \)) and \( 244 \) (which is \( a^2 + b^2 \)).

Since \( 225 \) is not equal to \( 244 \), we can conclude that:

**No, the triangle with sides 15, 10, and 12 is not a right triangle.**