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.

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

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:

And thus

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

So, the longest side is 12. Since the small is half the long, we have . Finally, the medium is three more of the small, so we have

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

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

So, we have

Hence, shorter side is 6 meters.

longer side is meters

medium side is   meters.

step-by-step explanation: