Solve for x. Round to the nearest hundredth

D

Step-by-step explanation:

We name the corners of the triangle as the attached image.

As we can see, triangle ABC is a right-angled triangle with Angle B equal to 90 degree.

As ABC is a right triangle, so that total measures of angle A and angle C is 90 degree

=> m∠A + m∠C = 90

=> m∠A + 45 = 90

=> m∠A = 90 - 45 = 45

=> m∠A = m∠C

So that ABC is also an isosceles triangle.

=> AB = AC  = x

As ABC is a right triangle, according to Pythagoras theorem, we have the following equation:

AB^2 + BC^2 = AC^2

=> x^2 + x^2 = 20^2

=> 2.x^2 = 400

=> x^2 = 400/2 = 200

=> x = ≈ 14.14

So that x ≈ 14.14, the correct answer is D

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

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