Answer:
x=14
PN=MN=85
Step-by-step explanation:
It is an isosceles triangle because PQ=MQ and QN is perpendicular to PM. PN=MN
8x-27=6x+1
2x=28
x=14
PN=MN=85
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Using Pythagorean theorem, we can justify our answer.
if c^2 = a^2 + b^2 then triangle is right one,
if c^2 > a^2 + b^2 then triangle is obtuse and
if c^2 < a^2 + b^2 then triangle is acute triangle.
Here a=8, b=11 and c=16
Put these values in the equation
16^2 = 8 ^2 + 11^2
256 = 64 +121
256> 185
So here c^2 > a^2 + b^2 Which means triangle is obtuse triangle.
Answer: Obtuse Triangle