Question

Given: △MOP, Perimeter of △MOP=12+4 sqr rt. 3 m∠P=90°, m∠M=60° Find: MP

Answer 1

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,

$PO^2+MP^2=MO^2\Rightarrow PO^2=(2x)^2-x^2=4x^2-x^2=3x^2\Rightarrow PO=\sqrt{3}x.$

The perimeter of triangle MOP is

$P_{MOP}=MO+PO+MP=x+2x+\sqrt{3}x=3x+\sqrt{3}x.$

Since $P_{MOP}=12+4\sqrt{3},$ then $x=4.$

Answer: MP=4 units.

Answer 2

Answer: Mp = 4 units

Step-by-step explanation:

Sorry I just know from RSM, I can't give you a detailed explanation. Hope this Helps!

-Vikii