Can someone please help me with this?

Mathematics

1 answer:

podryga [215]3 years ago

4 0

9514 1404 393

Answer:

x = 3

Step-by-step explanation:

Tangents to a circle from the same point are the same length.

43 -2x = 12x +1

42 = 14x . . . . . . . add 2x-1

3 = x . . . . . . . divide by 14

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the figure below is a square . Find the length of side x in simplest radical form with a rational denominator.

wel

Answer:

$\sqrt{14}$

Step-by-step explanation:

In any square with side length $s$ , the diagonal of the square is equal to $s\sqrt{2}$ . Since the side length of this square is $\sqrt{7}$ , the diagonal is equal to $\sqrt{7}\cdot \sqrt{2}=\boxed{\sqrt{14}}$ .

Alternatively, you can form two 45-45-90 triangles with the diagonal of the square. The diagonal acts as the hypotenuse for the both these triangles, and the legs of both triangles are equal to the side length of the square. To find the length of the diagonal, use the Pythagorean Theorem, which states $a^2+b^2=c^2$ , where $c$ is the hypotenuse of the triangle, and $a$ and $b$ are the two legs of the triangle.