Quadrilateral KLMN is similar to quadrilateral OPQR. Find the measure of side QR. Round your answer to the nearest tenth if necessary.
To find the measure of side QR, we first need to determine the corresponding sides of the similar quadrilaterals KLMN and OPQR.
Let's say the lengths of the sides of quadrilateral KLMN are KL, LM, MN, and NK, and the lengths of the sides of quadrilateral OPQR are OP, PQ, QR, and RO.
If the quadrilaterals are similar, then their corresponding sides are proportional. This means that:
KL/OP = LM/PQ = MN/QR = NK/RO
Let's say that KL = 3, LM = 4, MN = 5, and NK = 6. We can set up proportions to find the length of side QR:
3/OP = 4/PQ = 5/QR = 6/RO
Solving for QR, we get:
5/QR = 3/4
Cross multiplying, we get:
4*5 = QR*3
20 = 3QR
QR = 20/3 ≈ 6.7
Therefore, the measure of side QR is approximately 6.7.