Question

Solve for X, Leave in simplest radical form.

Answer 1

12

Explanation:

1) FInd the sides of small triangle. Since it has 2 congruent angles it also has to congruent sides opposite those angles. So the sides adjacent (connected to) the right angle are both 6.

2) Find the hypotenuse (side opposite the right angle) in the small triangle

a^2 +b^2 = c^2

6^2 +6^2 = c^2

36+36 = c^2

72 = c^2

c =
`√(72)`

In simplified radical form
`\sqrt{72\\` = 6
`√(2)`

3) Now find the sides of big triangle. It has 2 congruent angles therefore it has two congruent side opposite those angles. We know that one of the sides is 6
`√(2)` because it is also the hypotenuse of the small triangle. The other side adjacent to the right angle is also 6
`√(2)`.

4) Now find x which is the hypotenuse of the big triangle.

`(6√(2) )^(2)`+
`(6√(2) )^(2)`=
`c^(2)`

(36*2)+(36*2) =
`c^(2)`

144 =
`c^(2)`

c = 12

so x = 12