MATH SOLVE

4 months ago

Q:
# Two legs are 3√2. The triangle is 45-45-90. What is the hypotenuse?A. 6B. 18C. 12D. 5

Accepted Solution

A:

The answer is: [A]: "6" .

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Explanation:

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Using the Pythagorean theorem to solve for the hypotenuse of a right triangle:

a² + b² = c² ;

in which "c" is the length of the "hypotenuse" (for which we are to solve);

& "a" and "b" are the lengths of the other 2 (two) sides.

In this case, "a" and "b" are "equal lengths" ;

that is: a = b = 3√2 ;

So "(3√2)² + (3√2)² = c² " ; Solve for "c" ;

↔ c² = (3√2)² + (3√2)² ;

→ c² = 2*(3√2)² = 2 * (3²) * (√2)² ;

= 2 * 9 * 2 ;

= 18 * 2 = 36 ;

→ c² = 36 ;

Take the positive square root of each side of the equation ; to isolate "c" on one side of the equation ; & to solve for "c" (the length of the hypotenuse);

→ +√(c²) = +√36 ;

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→ c = 6 ; which is: "Answer choice: [A]: "6" .

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________________________________________________________

Explanation:

________________________________________________________

Using the Pythagorean theorem to solve for the hypotenuse of a right triangle:

a² + b² = c² ;

in which "c" is the length of the "hypotenuse" (for which we are to solve);

& "a" and "b" are the lengths of the other 2 (two) sides.

In this case, "a" and "b" are "equal lengths" ;

that is: a = b = 3√2 ;

So "(3√2)² + (3√2)² = c² " ; Solve for "c" ;

↔ c² = (3√2)² + (3√2)² ;

→ c² = 2*(3√2)² = 2 * (3²) * (√2)² ;

= 2 * 9 * 2 ;

= 18 * 2 = 36 ;

→ c² = 36 ;

Take the positive square root of each side of the equation ; to isolate "c" on one side of the equation ; & to solve for "c" (the length of the hypotenuse);

→ +√(c²) = +√36 ;

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→ c = 6 ; which is: "Answer choice: [A]: "6" .

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