Question

The perimeter of a triangle is 41 inches. The three sides of the triangle are all differnt lenghts. The longest side is 10 less than twice the middle side length. The middle side length is three less then three times the shortest side length. How long is aceh side of the triangle

Answer 1

`Longest\ side=20\ inches\\\\Middle\ side=15\ inches\\\\Shortest\ side=6\ inches`

Explanation:

Let be "x" the lenght of the longest side, "y" the lenght of the middle side and "z" the lenght of the shortest side.

The perimeter is:

`41=x+y+z` [Equation 1]

We know that the longest side is 10 less than twice the middle side length. This can be expressed as:

`x=2y-10` [Equation 2]

And the middle side length is three less than three times the shortest side length. This is:

`y=3z-3` [Equation 3]

The steps are:

- Solve for "z" from the third equation:

`y=3z-3\\\\y+3=3z`

`z=(y+3)/(3)` [Equation 4]

- Substitute [Equation 4] into [Equation 1]

- Substitute [Equation 2] into [Equation 1]

Then:

`41=(2y-10)+y+((y+3)/(3))`

- Solve for "y":

`41=2y-10+y+(y+3)/(3)\\\\41=2y-10+y+(y)/(3)+1\\\\41=(10)/(3)y-9\\\\41+9=(10)/(3)y\\\\(50*3)/(10)=y\\\\y=(150)/(10)\\\\y=15`

- Substitute this value into [Equation 2] and into [Equation 4]:

`x=2(15)-10\\\\x=20`

`z=((15)+3)/(3)\\\\z=6`