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The following trapezoids are similar. What is the value of
x ?

The following trapezoids are similar. What is the value of $x$ ?

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Absolute value and opposite integers

Full solution

Q. The following trapezoids are similar. What is the value of

x

?

Set up proportion: Since the trapezoids are similar, corresponding sides are proportional. Set up a proportion using the lengths of the corresponding sides.
Identify lengths: Let's say the lengths of the smaller trapezoid are $a$ and $b$ , and the lengths of the larger trapezoid are $c$ and $x$ . The proportion is $\frac{a}{b} = \frac{c}{x}$ .
Plug in values: Plug in the known values into the proportion. If $a = 5$ , $b = 10$ , and $c = 15$ , then it's $\frac{5}{10} = \frac{15}{x}$ .
Cross-multiply: Solve for $x$ by cross-multiplying: $5x = 15 \times 10$ .
Solve for x: Do the multiplication: $5x = 150$ .
Divide by $5$ : Divide both sides by $5$ to solve for x: $x = \frac{150}{5}$ .
Calculate result: Calculate the division: $x = \frac{30}{y}$ .

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