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

Sagot :

MrRoyal

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:

[tex]AB= 2x - 16[/tex]

[tex]BC= 3x - 19[/tex]

[tex]AC = 30[/tex]

The above parameters means that:

[tex]AB + BC = AC[/tex]

So, we have:

[tex]2x - 16 + 3x - 19 = 30[/tex]

Collect like terms

[tex]2x + 3x = 30 + 19 + 16[/tex]

[tex]5x = 65[/tex]

Divide both sides by 5

[tex]x = 13[/tex]

Substitute 13 for x in [tex]AB= 2x - 16[/tex] and [tex]BC= 3x - 19[/tex]

[tex]AB = 2 \times 13 - 16[/tex]

[tex]AB = 26 - 16[/tex]

[tex]AB = 10[/tex]

[tex]BC= 3x - 19[/tex]

[tex]BC= 3 \times 13 - 19[/tex]

[tex]BC= 39 - 19[/tex]

[tex]BC= 20[/tex]

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

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