Question

If a right triangle has sides 5, 12, and 13 units, then a triangle with sides 10, 24, and 26 is also a right triangle. True or False

Answer 1

True.

To determine if the triangle with sides 10, 24, and 26 is a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), the following equation holds:

\[
a^2 + b^2 = c^2
\]

First, we identify the sides of the triangle:
- \(a = 10\)
- \(b = 24\)
- \(c = 26\)

Now we square the lengths of the sides:

\[
10^2 + 24^2 = 100 + 576 = 676
\]
\[
26^2 = 676
\]

Since \(10^2 + 24^2 = 26^2\), we find that:

\[
676 = 676
\]

Therefore, the triangle with sides 10, 24, and 26 satisfies the Pythagorean theorem, confirming it is a right triangle.

Thus, the statement is **True**.