Question

Please answer asap and explain

Answer 1

The length of one of the legs is 3, so the length of the hypotenuse is √2 times 3, or D. 6√2. Therefore, D. 6√2 is correct.

Since the triangle is a 45-45-90 triangle, we know that the hypotenuse is

√2 times longer than either leg.

Therefore, the length of the leg opposite to the angle labeled x is 312/ √2 =212.

Now, we can use the Pythagorean Theorem to solve for x.

$x^2 =
`212^(2)` +
`212^2$`

$x^2 =
`90496$`

$x =
`√(90496)$`

$x =
`6√(2508)$`

$x =
`6√(2)` .
`√(1254)$`

$x =
`6√(2)` .
`21√(6)$`

$x =
`126√(12)$`

Therefore, the value of x is 126 12 , which is equivalent to 6 √2 .

We can also check our answer by looking at the answer choices.

The only answer choice that is a multiple of √2 is (D) 6√2 .