Remember for some side lengths to be part of a right triangle, they have to satisfy the Pythagorean Theorem, which is:
[tex]a^2 + b^2 = c^2[/tex]
Let's test the various side lengths to see if they satisfy the equation:
[tex]14^2 + 26^2 \stackrel{?}{=} 28^2[/tex]
[tex]196 + 676 \stackrel{?}{=} 784[/tex]
[tex]872 \neq 784[/tex]
The first group of side lengths does not work.
Let's try the other side lengths:
[tex]30^2 + 72^2 \stackrel{?}{=} 78^2[/tex]
[tex]900 + 5184 \stackrel{?}{=} 6084[/tex]
[tex]6084 = 6084 \,\,\checkmark[/tex]
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:
The third statement is true because it fulfills the Pythagorean theorem
Step-by-step explanation:
The sides of a right angled triangle will satisfy the Pythagorean theorem which is
[tex]a ^{2} + b^{2} = c^{2}[/tex]
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 )
