SOLUTION: 5) The first side of a triangle is 5 inches less than the second side, and the third side is twice as long as the first sides. If the perimeter of the triangle is 33 iches, find th

Click here to see ALL problems on Systems-of-equations

Question 75645: 5) The first side of a triangle is 5 inches less than the second side, and the third side is twice as long as the first sides. If the perimeter of the triangle is 33 iches, find the lengths of the sides of the triangle.
6) The shortest side of a triangle is 8 feet less than the medium side, and the longest side is 4 feetlonger than 3 times the shortest side. If the perimeter is 27 feet, find the length of the shortest side.

Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
LET X BE THE SECOND SIDE
X-5 IS THE FIRST SIDE
2(X-5) IS THE THIRD SIDE
NOW WE ADD ALL THREE SIDES & SET THEM EQUAL TO 33
X+(X-5)+2(X-5)=33
4X-5-10=33
4X=33+15
4X=48
X=48/4
X=12 INCHES FOR THE FIRST SIDE
12-5=7 FOR THE SECOND SIDE &
2(12-5)=2*7=14 FOR THE THIRD SIDE
PROOF
12+7+14=33
33=33
-------------------------------------------------------
LET M=MEDIUM SIDE
M-8=SHORTEST SIDE
3(M-8)+4=LONGEST SIDE
M+(M-8)+3(M-8)+4=27
M+M-8+3M-24+4=27
5M=27+8+24-4
5M=55
M=55/5
M=11 THE MEDIUM SIDE
THE SHORTEST SIDE IS 11-8=3 FEET.