Question 121608: In a triangle whose perimeter is 40 cm, the length of the longest side is four cm less than the sum of th lengths of the other sides. The length of the shortest side is four cm more than the difference between the lengths of the other sides. What is the length of the longest side?
Found 3 solutions by stanbon, checkley71, oscargut:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a triangle whose perimeter is 40 cm,
the length of the longest side is four cm less than the sum of th lengths of the other sides.
The length of the shortest side is four cm more than the difference between the lengths of the other sides.
What is the length of the longest side?
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Let the sides be x,y,z; x be the shortest, z be the longest.
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x+y+z = 40 cm
z = (x+y)-4
x = 2(z-y)
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Rearrange:
x+y+z = 40
x+y-z = 4
x+2y-2z=0
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Using the Matrix function of a TI caluculator I get:
x = 8 (shortest)
y = 14
z = 18 (longest)
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Cheers,
Stan H.
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website! LONGEST SIDE (C)=(A+B-4)
SHORTEST SIDE (A)=4+(A+B-4)-B
THE THREE SIDES ARE:(C)(A+B-4), (A)[4+(A+B-4)-B & (B)
40=A+B-4+4+A+B-4-B+B
40=2A+2B-4
2A+2B-4-40=0
2A=2B-44=0
2(A+B-22)=0
A+B-22=0
A+B=22
C=(A+B)-4
C=22-4
C=18 CM IS THE LONGEST SIDE.
Answer by oscargut(2103)  (Show Source):
You can put this solution on YOUR website! if a,b and c are the names of the sides (in decreasing order)
then
a+b+c=40 (1st equation)
(perimeter is 40 cm)
a=b+c-4 (2nd equation)
(the length of the longest side is four cm less than the sum of th lengths of the other sides)
c=a-b+4 (3rd equation)
(The length of the shortest side is four cm more than the difference between the lengths of the other sides.)
Resuming:
a+b+c=40 (1st equation)
a=b+c-4 (2nd equation) then b+c=a+4
c=a-b+4 (3rd equation) then b+c=a+4
look that 2nd and 3rd equations are the same thing
so we can not determine the sides b and c but.....
doing a substitution in the 1st equation we have:
a+(a+4)=40 so 2a+4=40 and a=18
Then the length of the longest side is 18 cms
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