Question

TIMED PICTURE INCLUDED

Answer 1

This is a special type of triangle, one which sides can easily be found. This is the 45-45-90 triangle, named by its angles: two 45 degree angles and one right angle.

In the 45-45-90 triangle, the two sides other than the hypotenuse can be represented by
`x` and the hypotenuse can be represented by
`x√(2)`.

This means that the length of the hypotenuse is the length of the smaller sides multiplied by the square root of 2. This is given to us by the Pythagorean Theorem (where x is the length of the smaller sides and y is the length of the hypotenuse):

`x^2 + x^2 = y^2 \Rightarrow 2x^2 = y^2 \Rightarrow x√(2) = y`

Thus, we can simply multiply the length of the smaller side (8) by the square root of 2 to get our answer of
`\boxed{8√(2)}`.

Answer 2

It has to be D , because the value of x is greater than 8 because the line is longer so none of the other choices work because they are all smaller .

Hope this helps!