Triangle perimeter

Question

a triangle has a perimeter of 31 inches. the longest side is twice as long as the shortest side. the 3rd side is 3 inches longer than the shortest side. how long is each side?

Answer 1

Hi Gabriele,

 

Let's translate the English into math.

 

Let the shortest side length = X

Let the longest side length = Z

Let the 3rd side length = Y

 

The triangle has a perimeter of 31 inches.  That means that X+Y+Z=31

The longest side is twice as long as the shortest side.  That means that 2X = Z

The 3rd side is 3 inches longer than the shortest side.  That means that X+3=Y

 

Now we have three equations to solve for three variables. We can substitute values for Y and Z into the first equation.

 

The second equation says that 2X = Z so we can rewrite the first equation as X+Y+2X=31

 

The third equation says that Y=X+3 so we can rewrite the first equation as X+X=3+2X=31

 

Now combine like terms-->4X+3=31

 

Subtract 3 from both side-->4X=28

 

Divide both sides by 4-->X=7

 

That means (from the second equation) Z=14

 

And from the third equation Y= 10

 

Reread the problem and substitute these numbers to make sure that they work.

 

Have fun.

 

Dan