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△ABC ~ △DBE

By looking at the order that the letters are given in the triangle names, we can say that

AC / DE = BC / BE

Since AC = 12 we can substitute 12 in for AC

12 / DE = BC / BE

Since DE = 4 we can substitute 4 in for DE

12 / 4 = BC / BE

Since BE = x we can substitute x in for BE

12 / 4 = BC / x

Since BC = BE + EC we can substitute BE + EC in for BC

12 / 4 = (BE + EC) / x

Since BE = x we can substitute x in for BE, and since EC = 6 we can substitute 6 in for EC

12 / 4 = (x + 6) / x

Now we just have to solve this equation for x. First let's simplify 12 / 4

3 = (x + 6) / x

Multiply both sides of the equation by x

3x = x + 6

Subtract x from both sides of the equation

3x - x = 6

3 apples - 1 apple = 2 apples, so 3x - x = 2x

2x = 6

Divide both sides by 2

x = 3

hectictar Sep 6, 2020