Question

a triangle has sides with lengths of 41 miles, 86 miles, and 90 miles. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides $a$, $b$, and hypotenuse $c$, $a^{2}+b^{2}=c^{2}$. Let $a = 41$, $b = 86$, and $c = 90$.

Step2: Calculate $a^{2}+b^{2}$

$a^{2}+b^{2}=41^{2}+86^{2}=1681 + 7396=9077$.

Step3: Calculate $c^{2}$

$c^{2}=90^{2}=8100$.

Step4: Compare

Since $a^{2}+b^{2}=9077
eq8100 = c^{2}$, the triangle is not a right - triangle.

Answer:

no