Math, asked by mohanasubanandini, 5 hours ago

Which of the following could represent the lengths of the sides of the triangle shown below?


PLS GIVE A BRILLIANT ANSWER
DON'T GIVE AN RUBBISH ONE​

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Answered by user0888
47

\huge\text{\underline{Solution}}

We have a right triangle. The Pythagorean theorem states that the sum of the squares of two sides is equal to the hypotenuse squared in a right triangle.

The three sides must follow the Pythagorean theorem converse. Converse means that if the triangle is right-angled, we always get the true equation.

\large{\red{\bold{\underline{Option\ A\ is\ incorrect.}}}}

\hookrightarrow6^{2}+8^{2}\neq12^{2}

\large{\red{\bold{\underline{Option\ B\ is\ incorrect.}}}}

\hookrightarrow4^{2}+5^{2}\neq6^{2}

\large{\green{\bold{\underline{Option\ C\ is\ correct.}}}}

\hookrightarrow9^{2}+12^{2}=15^{2}

\large{\red{\bold{\underline{Option\ D\ is\ incorrect.}}}}

\hookrightarrow4^{2}+8^{2}\neq10^{2}

So, option C is right.

\huge\text{\underline{Learn More}}

(a,b,c) is a Pythagorean triple. Then, for a positive number k, (ka,kb,kc) is also a Pythagorean triple, as two triangles are similar.

Let's bring an example, a Pythagorean triple (3,4,5). If we triple the lengths, we get (9,12,15) which was our answer.

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