Please help me solve this problem

Question

A triangle lot is formed where Main Street intersects Park Avenue. The owner of the lot has erected a fence around the entire perimeter of the lot, using a total of 500 linear feet of fencing. All three sides are different lengths, with side 2 being 25 feet less than twice the length of side 1, with side 3 being 100 feet longer than side 2. Find the lengths of the three sides

Answer 1

Let the lengths of the three sides be A, B, and C.

The perimeter = 500 ft = A + B + C

 

Also,

  B = -25 + 2A

  C = 100 + B

 

O.K. find A, B, C:

 

    A +        B     +           C                = 500

    A  +       B     +   100 +      B         = 500

    A + (2A - 25) + (100 + (2A - 25) ) = 500

      5A  + 50 = 500                       (collect terms)

          5A = 450                 (subtract 50 from both sides)

           A = 90              (divide both sides by 5)

 

    B = 2A - 25

    B = 2(90) - 25

    B = 155

 

    C = 100 + B

    C = 100 + 155

    C = 255

 

Checking (very important):

   Is  90 + 155 + 255 = 500    ?

              500 = 500   ? yes

 

  Is  155 = 2(90) - 25   ?

        155 = 155   ?  yes

 

  Is  255 = 100 + 155  ?  yes

Answer 2

Hi Bryn

 

let x = side 1

 

then side 2 = x - 25 ( 25 feet less than side 1

 

and side 3 = (x-25) + 100  (side 3 is 100 more than side 2 which is (x-25)

 

now add them up to find x

 

side 1 + side 2 + side 3 = 500

 

x + (x-25) + (x-25+100) = 500

 

3x + 50 = 500

 

3x = 450

 

x = 150  - side 1

 

x-25 = 125  - side 2

 

x -25 + 100 = 225 - side 3

 

150 + 125 + 225 = 500    and it all checks out

 

Hope this helps

 

Tom