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

Explanation:

Step1: Set up proportion for similar triangles

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

Step2: Cross-multiply to eliminate fractions

$7(x+4) = 9x$

Step3: Expand left side of equation

$7x + 28 = 9x$

Step4: Isolate x term

$28 = 9x - 7x$

Step5: Simplify and solve for x

$2x = 28 \implies x = \frac{28}{2} = 14$

Step6: Calculate scale factor

Scale factor (left to right) is $\frac{x}{7} = \frac{14}{7} = 2$

Answer:

$x = 14$
Scale factor of left triangle to right triangle is $2$