Question

in the diagram to the right,
$\triangle wlj\sim \triangle qbv$.
find the value of x. give the scale
factor of the left triangle to the right
triangle.
(the figures are not to scale.)

$x = 14$ (type an integer or a decimal.)

the scale factor of $\triangle wlj$ to $\triangle qbv$ is $\square: \square$.
(simplify your answers. type whole numbers.)

Explanation:

Step1: Set up proportion for similar triangles

Since $\triangle WLJ \sim \triangle QBV$, corresponding sides are proportional: $\frac{x}{7} = \frac{x+4}{9}$

Step2: Cross-multiply to solve for x

$9x = 7(x+4)$
$9x = 7x + 28$
$9x - 7x = 28$
$2x = 28$
$x = \frac{28}{2} = 14$

Step3: Calculate scale factor

Use corresponding sides $x=14$ and 7: $\frac{14}{7} = 2$

Answer:

$x = 14$
The scale factor of $\triangle WLJ$ to $\triangle QBV$ is $2:1$