How do you determine if the lengths 9, 40, 41 form a right triangle?

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How do you determine if the lengths 9, 40, 41 form a right triangle?

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Answer 1 · 2017-01-06T19:05:54

Following the Pythagorean theorem, 9, 40, and 41 form a right triangle.

Explanation:

Every right triangle follows the $a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$ format (also called the Pythagorean theorem).

$a$ $a$ and $b$ $b$ represent the two bases, which are also the two shorter sides. In this case, $a$ $a$ could represent 9 and $b$ $b$ could represent 40.

$c$ $c$ in the equation is the variable for the hypotenuse, which is the longest length in a right triangle. Plug in 41 for $c$ $c$ .

So $a = 9$ $a = 9$ , $b = 40$ $b = 40$ , and $c = 41$ $c=41$

Now you'd test if $9^{2} + 40^{2} = 41^{2}$ $9^2 + 40^2 = 41^2$

We'd solve, and get $81 + 1600 = 1681$ $81 + 1600 = 1681$

Because $81 + 1600$ $81+1600$ does equal $1681$ $1681$ , 9, 40, and 41 are the three lengths of one right triangle.

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How do you determine if the lengths 9, 40, 41 form a right triangle?

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