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9514 1404 393

  x = 1/2

Step-by-step explanation:

There are some different ways to find the area of a donut shape. One is to multiply its centerline length by its width. We'll use that here to find the shaded area of the sector.

The centerline radius of shaded area A is ...

  (6x -2) cm + (1/2)(4x cm) = 8x -2 cm

The length of the centerline is ...

  s = rθ = (8x -2)(π/4) . . . . . . for a central angle of 45° = π/4 radians

Then the area A is ...

  area A = (π/4)(8x -2)(4x) = 2πx(4x -1) . . . cm^2

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The radius of circle B is ((4 -4x) cm)/2 = (2 -2x) cm. The area of circle B is ...

  A = πr^2 = π(2 -2x)^2 cm^2

We're told the two areas are equal, so we have ...

  2πx(4x -1) = π(2 -2x)^2 . . . . . . . expressions for the areas are equal

  8x^2 -2x = 4x^2 -8x +4 . . . . . . divide by π, eliminate parentheses

  4x^2 +6x -4 = 0 . . . . . . . . . . . . subtract the right-side expression

  2(2x -1)(x +2) = 0 . . . . . . . . . . . factor

  x = 1/2 or -2 . . . . . . . only the positive solution is useful here

The value of x is 1/2.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.