Question 194227: Hi!!! Im Very Confused with this problem:
The Longest side of a triangle is twice as long as the shortest side and 2cm longer than the third side. if the perimeter of the triangle is 33 cm, what is the lenght of each side?
Pls Help me!!! Thank you!!!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! The Longest side of a triangle is twice as long as the shortest side and 2cm longer than the third side. if the perimeter of the triangle is 33 cm, what is the lenght of each side?
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Let x = length of the longest side
y = length of the third side
z = length of the shortest side
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then
x = 2z
x = y+2
x+y+z = 33
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Rearranging terms:
x + 0y - 2z = 0
x - y + 0z = 2
x + y + z = 33
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Solving with Cramer's rule
Matrix of coefficients:
1 0 -2
1 -1 0
1 1 1
Determinant of coefficients:
(-1 - 0) - 2(1 + 1) = -1 -2(2) = -1 -4 = -5
.
Matrix of 'x':
0 0 -2
2 -1 0
33 1 1
Determinant of 'x':
-2(2+33) = -2(35) = -70
x = detx/detcoeff = -70/-5 = 14 cm
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Matrix of 'y':
1 0 -2
1 2 0
1 33 1
Determinant of 'y':
(2-0) - 2(33-2) = 2 - 2(31) = 2 -62 = -60
y = dety/detcoeff = -60/-5 = 12 cm
.
Matrix of 'z':
1 0 0
1 -1 2
1 1 33
Determinant of 'z':
(-33-2) = -35
z = detz/detcoeff = -35/-5 = 7 cm
.
The three sides are:
14 cm, 12 cm and 7 cm
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