Respuesta :
Answer:
The correct option is option C
It is the only one that makes a right-angled triangle
Explanation:
The dimensions that would make a right angle are the ones with the set of numbers that satisfies the Pythagorean theorem
The Pythagorean theorem state that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the opposite sides.
Knowing that the hypotenuse is always the longest side
Suppose x is the hypotenuse of a right angled triangle, and y and z are the opposite sides, then
[tex]x^2=y^2+z^2[/tex]Let us check the given options one after the other to see which one is a Pythagorean Triple (satisfies the Pythagorean theorem).
A.
10, 8, 7
[tex]\begin{gathered} 10^2=8^2+7^2 \\ 100=64+49 \\ 100\ne113 \\ \\ \text{Not a Pythagorean triple} \end{gathered}[/tex]B.
31, 20, 21
[tex]\begin{gathered} 31^2=20^2+21^2 \\ 961=400+441 \\ 961\ne841 \\ \\ \text{Not a Pythagorean triple} \end{gathered}[/tex]C.
9, 40, 41
[tex]\begin{gathered} 41^2=40^2+9^2 \\ 1681=1600+81 \\ 1681=1681 \\ \\ \text{ This is a Pythagorean triple} \end{gathered}[/tex]D.
11, 13, 5
[tex]\begin{gathered} 13^2=11^2+5^2 \\ 169=121+25 \\ 169\ne146 \\ \\ \text{Not a Pythagorean triple} \end{gathered}[/tex]