.What is the largest integer value of MO for which parallelogram MNOP will have an acute angle at P?

Question

anonymous · Answer

http://media.education2020.com/evresources/2004-04-01-03-00_files/i0320000.jpg

anonymous · Answer

A.11
B.12
 C.13
 D.14

anonymous · Answer

$\triangle MOP$ is an isosceles triangle with two sides equal... $\angle M=\angle O$ since sides MP=OP=9... we can use Sine Law or Cosine Law to solve for unknown side MO... apply differentiation for maximum or largest value of MO....

anonymous · Answer

ok... we can simplify the solution this way... if $\angle P=90$ or right angle... we can use Pythagorean Theorem to find MO...$$MO=\sqrt{9^2+9^2}=\sqrt{81+81}=\sqrt{162}=12.7279...$$and since the question is largest integer value... we can say it is 12...

anonymous · Answer

to have MO=13 or 14, the $m\angle p>90$... 12 is the largest integer value once $m\angle P<90$...

anonymous · Answer

hope you got it @Augbay ...

anonymous · Answer

A Pythagorean triple is said to be "primitive" if the greatest common divisor of a, b, and c is 1. Use trial and error to find a primitive Pythagorean triple other than (3, 4, 5).