Question

The longest side of a triangle is two times the shortest side, while the medium side is 3 meters more than the shortest side. The perimeter is 27 meters. Find the dimensions.

Answer 1

Let
`s,\ m\, l` be the short, medium and long side, respectively. If we translate all the information into formulas, we get the following system:

`\begin{cases} l = 2s\\ m=s+3\\ s+m+l = 27 \end{cases}`

Using the second equation, we can express the middle side in terms of the small one, and reduce the system to two equations in two unknowns:

`\begin{cases} l = 2s\\ s+(s+3)+l = 27 \end{cases}`

And thus

`\begin{cases} l = 2s\\2s+l = 24 \end{cases}`

But then again, using the first equation, the third becomes

`2s+l = 24 \iff l+l = 24 \iff 2l = 24 \iff l=12`

So, the longest side is 12. Since the small is half the long, we have
`s = 6`. Finally, the medium is three more of the small, so we have
`m = 6+3 = 9`

Answer 2

Shorter side is 6 meters, medium side is 9 meters and longest side is 12 meters.

Explanation:

Given: The longest side of a triangle is two times the shortest side, while the medium side is 3 meters more than the shortest side. The perimeter is 27 meters.

To find: Dimensions of the triangle.

Solution:

Let the smaller side of the rectangle be x meters.

So, larger side is 2x meters

medium side is
`x+3`

It is given that the perimeter of the rectangle is 27 meters.

So, we have

`x+2x+x+3=27`

`\implies 4x+3=27`

`\implies 4x=27-3`

`\implies 4x=24`

`\implies x=(24)/(4)`

`\implies x=6`

Hence, shorter side is 6 meters.

longer side is
`2(6)=12` meters

medium side is
`6+3=9` meters.