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

Answer:

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

Step-by-step 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

$x+2x+x+3=27$

$\implies 4x+3=27$

$\implies 4x=27-3$

$\implies 4x=24$

$\implies x=\frac{24}{4}$

$\implies x=6$

Hence, shorter side is 6 meters.

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

medium side is  $6+3=9$ meters.