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# Hard maths problem solving question

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In a right-angled triangle PQR the hypotenuse is the side PR.
The length of side PQ is 20 cm and the ratio RQ:PQ is 1:2
What is the length of the perpendicular from the hypotenuse to the point Q?
2. (Original post by student_1999)

In a right-angled triangle PQR the hypotenuse is the side PR.
The length of side PQ is 20 cm and the ratio RQ:PQ is 1:2
What is the length of the perpendicular from the hypotenuse to the point Q?
Use Pythagoras followed by the "area of a triangle" formula

or

Use Pythagoras followed by similar triangles considerations
4. (Original post by student_1999)

In a right-angled triangle PQR the hypotenuse is the side PR.
The length of side PQ is 20 cm and the ratio RQ:PQ is 1:2
What is the length of the perpendicular from the hypotenuse to the point Q?
Draw a diagram and do some working out to show us where you're getting stuck.
5. I have had a go at it, and this is my best guess. Using Similar triangles, I found the opposite of the second triangle which is the perpendicular distance from PR to Q. If you have any questions feel free to ask. Also I have a sneaking suspicion you're applying for Cambridge engineering.
I have had a go at it, and this is my best guess. Using Similar triangles, I found the opposite of the second triangle which is the perpendicular distance from PR to Q. If you have any questions feel free to ask. Also I have a sneaking suspicion you're applying for Cambridge engineering.
Omg thank you so much!!! And I'm actually applying for Cambridge natural sciences, but the engineering paper has similar question. Thank you anyone, you've saved me from a sleepless night

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