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sergiy2304 [10]
3 years ago
13

Can please someone help me? The question is in the picture. Thank you

Mathematics
1 answer:
maxonik [38]3 years ago
6 0

Answer:

C. 9\pi

Step-by-step explanation:

We proceed to solve for x by the Pythagorean Theorem:

(x+1)^{2} = (x-1)^{2} + (2\cdot x - 4)^{2} (1)

x^{2} + 2\cdot x + 1 = (x^{2}-2\cdot x + 1) + (4\cdot x^{2}-16\cdot x + 16)

x^{2} + 2\cdot x + 1 = 5\cdot x^{2}-18\cdot x  + 17

4\cdot x^{2} -20\cdot x + 16 = 0

(2\cdot x)^{2} -10\cdot (2\cdot x) + 16 = 0

(2\cdot x -8)\cdot (2\cdot x -2) = 0

There are two different solutions:

x_{1} = 4, x_{2} = 1

A solution of x is considered realistic when the length of every side of the triangle is a not negative number.

x_{1} = 4

UV = 2\cdot (4) - 4

UV = 4

WU = 4 - 1

WU = 3

WV = 4 + 1

WV = 5

x_{2} = 1

UV = 2\cdot (1) - 4

UV = -2

WU = 1 - 1

WU = 0

WV = 1 + 1

WV = 2

The only realistic set of solutions is for x = 4, and the radius of the circle is represented by the line segment WU: r = 3

And the area of the circle (A) is calculated from the following formula:

A = \pi\cdot r^{2}

A = \pi\cdot (9)

A = 9\pi

The correct answer is C.

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