Given: △mop, perimeter of △mop=12+4 sqr rt. 3 m∠p=90°, m∠m=60° find: mp

Consider triangle MOP. This triangle is right triangle, because  m∠P=90°.

Since  m∠P=90°, m∠M=60°, then m∠O=180°-90°-60°=30°.

The leg opposite to the angle with measure 30° is half of the hypotenuse. Let the leg MP=x, then the hypotenuse MO=2x. By the Pythagorean theorem,

The perimeter of triangle MOP is

Since then

MP=4 units.

2x^2+5x+17

your welcome. : )