Find the lengths of the missing sides in the triangle? If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.

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Answer 1 · 2018-03-22T05:06:42

# x=4, y=sqrt32=4sqrt2#.

Observe that the third angle of the triangle has measure of

#180^@-90^@-45^@=45^@.#

So, the triangle has two congruent angles, and as such the

sides opposite to them are also congruent.

#:. x=4.#

Thus, the right-isosceles triangle has sides of length #4, 4#

and the length of the hypotenuse is #y#.

By Pythagoras' Theorem, then,

#y^2=4^2+4^2=32 rArr y=sqrt32=4sqrt2#.