Answer:
The answer is that x = 0 and y = -6. While this is not any of your options, the work below proves that it is correct.
In order to find these values, we can use elimination. To do so, we multiply the first equation by 5 and then add the equations together.
125x - 5y = 30
-2x + 5y = -30
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123x = 0
x = 0
Now that we have this value, we can plug the value into one of the originals and find y.
25x - y = 6
25(0) - y = 6
-y = 6
y = -6
ANSWER

EXPLANATION
Since the altitude, |GJ| bisects the base of the triangle, it follows that, the triangle is an isosceles triangle.
This implies that,.

In terms of x, we have the equation.

We now group like terms to obtain,

This implies that,

Let us divide through by 2 to get,

We can see from the diagram that,

We substitute x=5 to get,

This simplifies to,

Let the width path be x.
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.
Combined Area = (2x + 26)*(2x + 8) = 1008
2x*(2x + 8) + 26*(2x + 8 ) = 1008
4x² + 16x + 52x + 208 = 1008
4x² + 68x + 208 - 1008 = 0
4x² + 68x - 800 = 0. Divide through by 4.
x² + 17x - 200 = 0 . This is a quadratic equation.
Multiply first and last coefficients: 1*-200 = -200
We look for two numbers that multiply to give -200, and add to give +17
Those two numbers are 25 and -8.
Check: 25*-8 = -200 25 + -8 = 17
We replace the middle term of +17x in the quadratic expression with 25x -8x
x² +17x - 200 = 0
x² + 25x - 8x - 200 = 0
x(x + 25) - 8(x + 25) = 0
(x+25)(x -8) = 0
x + 25 = 0 or x - 8 = 0
x = 0 -25 x = 0 + 8
x = -25 x = 8
The width of the path can not be negative.
The only valid solution is x = 8.
The width of the path is 8 meters.
Answer:
It would have to be (C) 50.27 because 25 is too short for a diameter of 8 seeing it would be 8x4 to get 32 in which 25 is not long enough for. So the answer is C.