Question

Determine whether the given lengths can be sides of a right triangle.

Which of the following are true statements.


The lengths 14, 24 and 26 can be sides of a right triangle. The lengths 30, 72, and 78 can not be sides of a right triangle.

The lengths 14, 24 and 26 can not be sides of a right triangle. The lengths 30, 72, and 78 can not be sides of a right triangle.

The lengths 14, 24 and 26 can not be sides of a right triangle. The lengths 30, 72, and 78 can be sides of a right triangle.

The lengths 14, 24 and 26 can be sides of a right triangle. The lengths 30, 72, and 78 can be sides of a right triangle. .

Answer 1

Remember for some side lengths to be part of a right triangle, they have to satisfy the Pythagorean Theorem, which is:

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

• 
  `a` and
  `b` are the legs of the triangle
• 
  `c` is the hypotenuse (the longest side)

Let's test the various side lengths to see if they satisfy the equation:

`14^2 + 26^2 \stackrel{?}{=} 28^2`

`196 + 676 \stackrel{?}{=} 784`

`872 \\eq 784`

The first group of side lengths does not work.

Let's try the other side lengths:

`30^2 + 72^2 \stackrel{?}{=} 78^2`

`900 + 5184 \stackrel{?}{=} 6084`

`6084 = 6084 \,\,\checkmark`

This group of side lengths checks out!

The answer would be Choice C, or The lengths 14, 24 and 26 can not be sides of a right triangle. The lengths 30, 72, and 78 can be sides of a right triangle.

Answer 2

The third statement is true because it fulfills the Pythagorean theorem

Explanation:

The sides of a right angled triangle will satisfy the Pythagorean theorem which is

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

where A and B are the sides of the Triangle named the opposite and adjacent sides to the right angle.

while C is the hypotenuse ( the longest side of a right angled triangle )

from the first statement:

14^2 + 24^2 = 26^2

196 + 576 = 676

772 ≠ 676 ( wrong statement )

from the second statement

30^ + 72^2 = 78^2

900 + 5184 = 6084

6084 = 6084 ( wrong statement )

from the third statement

14^2 +24^2 = 26^2

196 + 576 ≠676

and

30^2 + 72^2 = 78^2

6084 = 6084 ( correct statement )