Question 1194769: Pls help me solve this :
The lengths of the sides of a triangle are consecutive even integers. Find the
length of the longest side if it is 14 units shorter than the perimeter.
Pls also include Proving. Thank you!!! :)
Answer by amarjeeth123(569)   (Show Source):
You can put this solution on YOUR website! We are given that the lengths of the sides of a triangle are consecutive even integers.
Let the sides of the triangle be x,x+2 and x+4 respectively.
We are given that the length of the longest side is 14 units shorter than the perimeter.
The length of the longest side=x+4 units
The perimeter of the triangle = x+x+2+x+4=3x+6 units
Plugging in the values we get,
x+4=3x+6-14
x+4=3x-8
x+4+8=3x
x+12=3x
3x-x=12
2x=12
x=6 units
The longest side of the triangle is 6+4=10 units
The lengths of the triangle are 6,8 and 10 units respectively.
The perimeter of the triangle is 6+8+10=24 units
10=24-14
The longest side is 14 units shorter than the perimeter of the triangle.
Thus, the solution is correct.Hence,proved.
Hence,the longest side of the triangle is 10 units.
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