Parallel sides are sides that are equidistant from one another. The value of x is 1
Given that:
[tex]CQ = x + 2\\QA = x\\CP = 5x + 4\\PD = 3x[/tex]
Since:
QR & AB are parallel, and RP & BD are parallel.
Then by theorem of similarities:
[tex]\frac{CQ}{QA} = \frac{CP}{PD}[/tex]
This gives:
[tex]\frac{x+2}{x} = \frac{5x + 4}{3x}[/tex]
Multiply both sides by 3x
[tex]3x \times \frac{x+2}{x} = \frac{5x + 4}{3x} \times 3x[/tex]
[tex]3 \times (x+2) = 5x + 4[/tex]
Open bracket
[tex]3x+6 = 5x + 4[/tex]
Collect like terms
[tex]5x - 3x = 6 -4[/tex]
[tex]2x = 2[/tex]
Divide both sides by 2
[tex]x = 1[/tex]
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