In the parallelogram below, if AP = 45 and PC = 3x + 15, find x.

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03-11-2022
Mathematics

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In the parallelogram below, if AP = 45 and PC = 3x + 15, find x.

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AverylV403902 AverylV403902 · Answer 1 · 2022-11-03T17:14:57+01:00

One of the properties of a parallelogram is that its diagonals bisect each other. This means that one diagonal cuts the second diagonal in equal length.

This means that AP = PC. If AP = PC, then 45 = 3x + 15.

[tex]45=3x+15[/tex]

We can now find the value of x using the equation above.

First, subtract 15 on both sides of the equation.

[tex]45-15=3x+15-15[/tex][tex]30=3x[/tex]

Then, divide both sides of the equation by 3 to isolate x.

[tex]\frac{30}{3}=\frac{3x}{3}[/tex][tex]10=x[/tex]

Therefore, the value of x is 10. (Option B)