Question

What is the value of x?


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Answer 1

Since QC and BR are parallel, triangles CDQ and BDR are similar.

This means that corresponding sides are in proportion, so we have

$BD \div QD = RD \div CD$

Substituting numbers, we have

$26+39 \div 39 = 18+x \div x \iff \dfrac{65}{39} = \dfrac{18+x}{x}$

Multiply both sides by $39x$

$65x = 39(18+x)$

Expand right hand side:

$65x = 702 + 39x$

Subtract 39x from both sides:

$26x = 702$

Divide both sides by 26

$x = \dfrac{702}{26} = 27$

Answer 2

Just took the test and got the the correct answer *\(♡°▽°♡)/*

Look at the image down below!!