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A triangle has side lengths
=5m,sqrt12m,sqrt13m
A) Is the triangle a right triangle? (type yes or no in the blank)_
B) Give the number proof for your answer in "A" here
A triangle has side lengths
=5m,sqrt12m,sqrt13m

A triangle has side lengths $=5 m, \sqrt{12} m, \sqrt{13} m$ $\newline$ A) Is the triangle a right triangle? (type yes or no in the blank)_ $\newline$ B) Give the number proof for your answer in

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Find equations of tangent lines using limits

Full solution

Q. A triangle has side lengths

=5 m, \sqrt{12} m, \sqrt{13} m

\newline

A) Is the triangle a right triangle? (type yes or no in the blank)_

\newline

B) Give the number proof for your answer in

Use Pythagorean Theorem: To determine if the triangle is a right triangle, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. $c^2 = a^2 + b^2$
Square Side Lengths: Let's square the lengths of the sides: $\newline$ egin{equation}( $5$ m)^ $2$ = $25$ m^ $2$ , $\newline$ egin{equation}(\sqrt{ $12$ }m)^ $2$ = $12$ m^ $2$ , $\newline$ egin{equation}(\sqrt{ $13$ }m)^ $2$ = $13$ m^ $2$ .
Add Squares: Now, we add the squares of the two smaller sides to see if they equal the square of the largest side: $25m^2 + 12m^2 = 37m^2$ .
Compare Sums: We compare this sum to the square of the largest side: $37m^2 \neq 13m^2$ .

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