Question

quadrilateral ghij is similar to quadrilateral klmn. find kl. round your answer to the nearest tenth if necessary. figures are not drawn to scale.
(images of two quadrilaterals: ghij with jg=9, gh=14; klmn with nk=43, kl=x)

Explanation:

Step1: Set up similarity proportion

Corresponding sides of similar quadrilaterals are proportional. So $\frac{GH}{KL} = \frac{JG}{NK}$

Step2: Substitute known values

Substitute $GH=14$, $JG=9$, $NK=43$, $KL=x$:
$\frac{14}{x} = \frac{9}{43}$

Step3: Cross-multiply to solve for $x$

$9x = 14 \times 43$
$9x = 602$
$x = \frac{602}{9}$

Step4: Calculate and round

$x \approx 66.9$

Answer:

$66.9$