If one side of a triangle is one third the longest side and the third side is eight feet less than the longest side and the perimeter is 69, find all three side

Question

find all three sides.

Answer 1

Hi Donna from Hazard, KY...hope you had a great week at school.

A great Algebra/Geometry word problem...every student's favorite! Right?! NOT!!   Anyway...I'm going to help you get started in setting up this problem, so you'll be able to do these on your own, making you a pro.

Here we go...let's begin with identifying the things we know:

   we have a triangle...

    one side which we'll assume is the longest side, we'll label as    'x'

    we're told another side is one-third the longest side, so     1/3x  or  .3x

   the third side is 8ft less than the longest side, so   x - 8

   and lastly, the perimeter is 69 feet(I presume)

Now, we need to say what it is we are suppose to find. In this case, once we find out what 'x' is, we can put it into our unknowns a calculate the sides of the triangle.

Another thing we know is the perimeter...do you know what that is? You do need to know, if you don't know, you will not be able to solve this problem.

Expecting that you do know...we will proceed. However, if you did not, then make sure you know what these terms mean.

So...perimeter is the measure around the edges of an object, in this case the figure of a triangle. So, our formula is adding the sides..

   side  plus   side   plus  side  equals  perimeter    or

       side + side + side  = perimeter           now, substitute what we know

         x +  0.3x  + x - 8  =  69                   combine like terms

         x + x  +  0.3x - 8 = 69       

               2x +  0.3x - 8 = 69                  Combine like terms

               2x +  0.3x - 8  +  8   = 69  +  8

              2x +  0.3x  =  77

Okay...now you should be able to complete the rest. 

I have the answer however, you need to be able to complete the rest.

If you have any further issues, contact me on Wyzant

Answer 2

Let x = the length of the longest side

Let (1/3)x = the length of another side

Let x - 8 = the length of the third side

 

P = a + b + c

69 = x + (1/3)x + (x - 8)

69 =  (2 1/3)x - 8

77 = (7/3)x

x = 33 feet 

(1/3)x = 11 feet

x - 8 = 25 feet