Question

the triangles are similar. find the value for ( x ), and include the correct units.
figure is not drawn to scale
( x = ) 55 missing units
enter an integer or decimal number with units more...
question help: video message instructor

Explanation:

Step1: Set up proportion for similar triangles

Since the triangles are similar, their corresponding sides are proportional:
$\frac{x}{99\ \text{mi}} = \frac{45\ \text{yd}}{81\ \text{mi}}$

Step2: Solve for $x$

Multiply both sides by $99\ \text{mi}$ to isolate $x$:
$x = \frac{45\ \text{yd} \times 99\ \text{mi}}{81\ \text{mi}}$

Step3: Simplify the expression

Cancel the mile units, then calculate the numerical value:
$x = 45 \times \frac{99}{81}\ \text{yd} = 45 \times \frac{11}{9}\ \text{yd} = 55\ \text{yd}$

Answer:

$x = 55$ yd