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Sagot :
Let's determine if the given lengths form a right triangle.
To determine if they form right traingles, apply Pythagorean formula:
[tex]a^2+b^2=c^2[/tex]Let's solve for the following:
a) a, b, c = 9, 40, 41
Substitute 9 for a and 40 for b, if the result gives 41, this means the lengths form a right triangle.
We have:
[tex]\begin{gathered} 9^2+40^2=c^2 \\ \\ 81+1600=c^2 \\ \\ 1681=c^2 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{1681}=\sqrt[]{c^2} \\ \\ 41=c \end{gathered}[/tex]Since the value of c is 41, we can say the lengths form a right triangle.
[tex]9^2+40^2=41^2[/tex]b) 11, 60, 62
Apply pythagorean theorem:
[tex]\begin{gathered} 11^2+60^2=c^2 \\ \\ 121+3600=c^2 \\ \\ 3721=c^2 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{3721}=\sqrt[]{c^2} \\ \\ 61=c \end{gathered}[/tex]The value of c is not 62, this means the given lengths do not form a right triangle.
[tex]11^2+60^2\ne62^2[/tex]c) 48, 55, 73
Apply Pythgorean theorem
[tex]\begin{gathered} 48^2+55^2=c^2 \\ \\ 2304+3025=c^2 \\ \\ 5329=c^2 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{5329}=\sqrt[]{c^2} \\ \\ 73=c \end{gathered}[/tex]The value of c is 73, this means the given lengths form a right triangle.
[tex]48^2+55^2=73^2[/tex]ANSWER:
• a) Form a right triangle
• b) Do not form a right triangle
• c) Form a right triangle
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