Question

If AC = 10 cm and EC = 3x - 7, for what value of x is ABCD a parallelogram? Explain your reasoning.

Answer 1

Given a parallelogram

Theorem: the diagonals of a parallelogram bisect each other, hence we can conclude that

`\begin{gathered} |AC|=|AE|+|EC| \\ \text{Also} \\ |AE|=|EC| \\ \text{Thus,} \\ |AC|=|EC|+|EC| \\ |AC|=2|EC| \end{gathered}`

Since AC = 10, and EC = 3x - 7

Therefore

`\begin{gathered} 10=2(3x-7) \\ 10=6x-14 \\ 10+14=6x \\ 24=6x \\ 6x=24 \\ (6x)/(6)=(24)/(6) \\ x=4 \end{gathered}`

Hence, for ABCD to be a parallelogram, the value of x is 4