Question

quadrilateral klmn is similar to quadrilateral opqr. find the measure of side op. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

image of two rectangles: klmn with kn=17, kl=26; opqr with ro=55

Explanation:

Step1: Set up similarity proportion

Since similar quadrilaterals have proportional corresponding sides, we match side $NK$ to $RO$, and $KL$ to $OP$.
$\frac{NK}{RO} = \frac{KL}{OP}$

Step2: Substitute known values

Plug in $NK=17$, $RO=55$, $KL=26$.
$\frac{17}{55} = \frac{26}{OP}$

Step3: Solve for $OP$

Cross-multiply and isolate $OP$.
$OP = \frac{26 \times 55}{17}$

Step4: Calculate the value

Compute the numerator first, then divide.
$OP = \frac{1430}{17} \approx 84.1$

Answer:

$84.1$