Use $a^2 + b^2 = c^2$:

$3^2 + 4^2 = c^2$

$9 + 16 = c^2$

$25 = c^2$

$c = 5$

Answer: The hypotenuse is $5$

Use $a^2 + b^2 = c^2$:

$5^2 + b^2 = 13^2$

$25 + b^2 = 169$

$b^2 = 144$

$b = 12$

Answer: The other leg is $12$

Use $a^2 + b^2 = c^2$:

$5^2 + b^2 = 13^2$

$25 + b^2 = 169$

$b^2 = 144$

$b = 12$

Answer: The other leg is $12$

Use the converse of the Pythagorean Theorem.

Check if $a^2 + b^2 = c^2$ (where $c = 25$ is the longest side):

$7^2 + 24^2 = 49 + 576 = 625$

$25^2 = 625$

Since $7^2 + 24^2 = 25^2$, the triangle is a right triangle.

Answer: Yes, it is a right triangle (and $7, 24, 25$ is a Pythagorean triple)

Use the converse of the Pythagorean Theorem.

Check if $a^2 + b^2 = c^2$ (where $c = 25$ is the longest side):

$7^2 + 24^2 = 49 + 576 = 625$

$25^2 = 625$

Since $7^2 + 24^2 = 25^2$, the triangle is a right triangle.

Answer: Yes, it is a right triangle (and $7, 24, 25$ is a Pythagorean triple)