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# Math Matters: Problem of the week – Problem 4 solution

Test your mathematical skills with the Problems of the Week from the Spring 2018 issue of Math Matters magazine!

We solved Problems 1-3.
[Check your solution to Problem 1.](https://iastate.box.com/s/ksn1gldahyjlxnk59bllf29g3itfb9yk)
[Check your solution to Problem 2.](https://iastate.box.com/s/lfwhxa4b2avn1phm3l7m8u0kmrq2q91t)
[Check your solution to Problem 3.](https://iastate.box.com/s/r8zqykcivi84tftyy8j51uxo8j5l7no0)

You’ve been working on Problem 4.

Problem 4. In trapezoid PQRS, PQ and SR are perpendicular to PS, PQ < RS and PQ + RS = QR. Given that PS = 20, find the value of PQ * RS.

[Check your solution to Problem 4.](https://iastate.box.com/s/yneb8swx3yt84ofggedy18rcxp393qfv)

Was Problem 4 a chore or a bore? Our final challenge is Problem 5!

Problem 5. An ellipse in the plane has foci at (20; 19) and (55; 59) and is tangent to the y-axis. What is the length of the major axis of the ellipse?

Check back the first Monday of November for the answer to Problem 5!