Question

If AB = 2x-16, BC = 3x -19, and AC = 30, find the values of x, AB, and BC.

Answer 1

Line segments can be split into several subsegments.

The values of x, AB and BC are 13, 10 and 20, respectively.

The given parameters are:

$AB= 2x - 16$

$BC= 3x - 19$

$AC = 30$

The above parameters means that:

$AB + BC = AC$

So, we have:

$2x - 16 + 3x - 19 = 30$

Collect like terms

$2x + 3x = 30 + 19 + 16$

$5x = 65$

Divide both sides by 5

$x = 13$

Substitute 13 for x in $AB= 2x - 16$ and $BC= 3x - 19$

$AB = 2 \times 13 - 16$

$AB = 26 - 16$

$AB = 10$

$BC= 3x - 19$

$BC= 3 \times 13 - 19$

$BC= 39 - 19$

$BC= 20$

Hence, the values of x, AB and BC are 13, 10 and 20, respectively.

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