Question

In each case determine if the sides form a right triangle if the do place them i. the yes if they do not place them in the no column

a) 3, 4, 5
b) 5, 12, 13
c) 8, 15, 17
d) 7, 24, 25

Answer 1

To determine if the sides form a right triangle, we can use the Pythagorean theorem. The sides form a right triangle if the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side.

Step-by-step explanation:

In order to determine if the sides form a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

a) For the sides 3, 4, and 5, we can see that 3^2 + 4^2 = 9 + 16 = 25. Since 25 is equal to 5^2, the sides do form a right triangle.

b) For the sides 5, 12, and 13, we have 5^2 + 12^2 = 25 + 144 = 169. Since 169 is equal to 13^2, the sides do form a right triangle.

c) For the sides 8, 15, and 17, we have 8^2 + 15^2 = 64 + 225 = 289. Since 289 is equal to 17^2, the sides do form a right triangle.

d) For the sides 7, 24, and 25, we have 7^2 + 24^2 = 49 + 576 = 625. Since 625 is equal to 25^2, the sides do form a right triangle.