SOLUTION: 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.

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.
RELATED QUESTIONS
The lengths of the sides of a triangle are consecutive even integers. Find the length of... (answered by Alan3354)

the lengths of the sides of a triangle are consecutive even integers. The perimeter is 42 (answered by Alan3354)

The shortest side of a right triangle measures 6m. The length of the other two sides are (answered by advanced_Learner)

the perimeter of the triangle 63 units and the lengths of the sides of the triangle are... (answered by greenestamps)

A right triangle has sides whose lengths in feet are consecutive even integers. determine (answered by nerdybill)

The Lengths of the sides of a triangle are consecutive even integers. Find the length of... (answered by checkley77)

The lengths of the sides of a triangle are consecutive even integers. Find the length of (answered by edjones)

The lengths of the sides of a triangle are consecutive even integers. Find the length of... (answered by MathLover1)

the perimeter of a triangle is 72ft. if the lengths of the sides are consecutive even... (answered by Theo)