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frika

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,

[tex]PO^2+MP^2=MO^2\Rightarrow PO^2=(2x)^2-x^2=4x^2-x^2=3x^2\Rightarrow PO=\sqrt{3}x.[/tex]

The perimeter of triangle MOP is

[tex]P_{MOP}=MO+PO+MP=x+2x+\sqrt{3}x=3x+\sqrt{3}x.[/tex]

Since [tex]P_{MOP}=12+4\sqrt{3},[/tex] then [tex]x=4.[/tex]

Answer: MP=4 units.

alisonsham678

Answer:

mp=4 cuz in a 30-60-90 degree right triangle if the shorter leg is x, then the longer leg (po) is xsqrt3. Because the perimeter is 12+4sqrt3, that means the longer leg is probably 4sqrt3. because of this, then the shorter leg, mp is 4. Since the hypotenuse is equal to 2x, then it would be 2*4=8=PO.

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