A triangle has sides of length 6, 8, and 10. Is it a right triangle? Explain.

Mathematics

2 answers:

Anna35 [415]3 years ago

6 0

Answer:

yes because according to the Pythagorean theorem

Step-by-step explanation:

Ipatiy [6.2K]3 years ago

3 0

Yes it is, assuming we decide to use the Pythagorean Theorem to find the hypotenuse (10) it'll be possible considering the formula is c²=√a²+b²
(c being the longest side of the triangle)
a= 6 and b= 8

c² =√6² + 8²
c² = √100 square root of 100 equals 10
c= 10

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How to do this?

Mandarinka [93]

This equation uses two properties of logarithms:

$\ln(g^x) = x \ln(g)$

$\ln(a) + \ln(b) = \ln(ab)$

So you could take the ln from left and right hand side in the equation, and get:

(2-x)ln 3 = x ln 5

then

2 ln 3 - x ln 3 - x ln 5 = 0 =>

x(ln 3 + ln 5) = 2 ln 3

so x = 2 ln 3 / (ln3 + ln5)

Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15

so x= ln9 / ln15

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