SOLUTION: Geometry: Triangles if triangle MNP, MN= 4x+1, Np+7x-11, and MP= 11x-16. If the perimeter of triangle MNP is 84, order the angles from greatest. I need help please!

Click here to see ALL problems on Triangles

Question 1013118: Geometry: Triangles
if triangle MNP, MN= 4x+1, Np+7x-11, and MP= 11x-16. If the perimeter of triangle MNP is 84, order the angles from greatest. I need help please!
Found 2 solutions by macston, Boreal:
Answer by macston(5194) (Show Source):
You can put this solution on YOUR website!
.
I think you mean MN=4x+1; NP=7x-11; MP=11x-16
.
MN+NP+MP=84
(4x+1)+(7x-11)+(11x-16)=84
22x-26=84
22x=110
x=5
.
MN=4x+1=4(5)+1=21
.
NP=7x-11=7(5)-11=35-11=24
.
MP=11x-16=11(5)-16=55-16=39
.
MP>NP>MN
.

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
4x+1+7x-11+11x-16=84
22x-26=84
22x=110
x=5
It helps to draw this. I have MN as the base and P to the upper right of N. Angle A is P, angle B is M, angle C is N. Law of Cosines
MN is 21 (A)
NP=24 (B)
MP=39 C) C will be the biggest angle
c^2=a^2+b^2-2abcosC
1521=441+576-2(504) cos C
504=-2(504)cos C
cos C=-(1/2)=120 degrees.
=================
a^2=b^2+c^2-2bc cos A
441=576+1521-2(936) cos A
-1656= -1872 cos A
cos A=27.8 degrees Can assume the other angle is 32.2 but will check to be sure.
=================
b^2=a^2+c^2-2ac cos B
576=441+1521-2(819) cos B
-1386=-1638 cos B
cos B=32.2
The angle at N is the largest, the one at M the second largest, and the one at P the smallest.