Help with length of hypotenuse

Mathematics

2 answers:

Molodets [167]3 years ago

6 0

Answer:

sqrt(10)x so ten is your answer

Step-by-step explanation:

hope this helps

Salsk061 [2.6K]3 years ago

5 0

Answer:

sqrt(10) *x

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

x^2 + (3x)^2 = hypotenuse ^2

x^2 + 9x^2 = hypotenuse ^2

10x^2 = hypotenuse ^2

Take the square root of each side

sqrt( 10x^2) = sqrt(hypotenuse ^2)

sqrt(10) * x = hypotenuse

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Readme [11.4K]

For this case we have to define root properties:

$\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a$

In addition, we know that:

$a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}$

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Thus, we can rewrite the given expression as:

$\sqrt {4 ^ 2 * a ^ 8 * \frac {1} {b ^ 2}} =\\4 ^ {\frac {2} {2}} * a ^ {\frac {8} {2}} * \frac {1} {b ^ {\frac {2} {2}}} =\\4 * a ^ 4 * \frac {1} {b}$