Question

find the unknown side length labeled with a variable in the given pair of similar triangles.
diagram of two right triangles with hypotenuses 27 and 30, one leg 18, the other leg x
x = \square
(simplify your answer.)

Explanation:

Step1: Set up proportion for similar triangles

Since the triangles are similar, the ratios of corresponding sides are equal. So, $\frac{18}{x} = \frac{27}{30}$.

Step2: Cross - multiply to solve for x

Cross - multiplying gives $27x = 18\times30$. First, calculate $18\times30 = 540$. Then, we have the equation $27x = 540$.

Step3: Divide both sides by 27

To find $x$, divide both sides of the equation $27x = 540$ by 27. So, $x=\frac{540}{27}$. Simplifying $\frac{540}{27}$, we get $x = 20$.

Answer:

20