Algebra word problems

Question

One side of an equilateral triangle is 6 ft shorter than one side of a square. The difference between the two perimeters is 28 ft. Find the perimeter of each figure

Answer 1

3a=perimeter of triangle (a+b+c where all sides same)

4s=perimeter of square

a=s-6..triangle in relation to square

3(s-6)=3s-18

4s-(3s-18)=28...difference in perimeters (note (-)(-) is +)

s+18=28

 -18=-18...add

=======

s=10...side of square

a=10-6=4...side of triangle 

 

Square= 4(10)=40ft=perimeter

Triangle= 4+4+4=12ft=perimeter 

 

Answer 2

Equilateral triangles and squares each have sides of equal length.  So we can set the following variables as

 

Let length of square = x

Let length of equilateral triangle = x - 6

 

 

The perimeter is the sum of all the sides of a shape.

 

Perimeter of a square is  4x     

  (four equal sides)

 

Perimeter of an equilateral triangle is  3(x - 6) = 3x - 18       

             (three equal sides)

 

 

The difference between their perimeters is 28 ft.  So we have

 

4x - (3x - 18) = 28

 

4x - 3x + 18 = 28

x + 18 = 28

x = 10

 

 

Substitute this x value into the length of each shape.

 

Length of square = 10 ft

Length of equilateral triangle = 4 ft

 

 

Now we can find the perimeter of each shape.

 

Perimeter of square = 4(10) = 40 ft

 

Perimeter of equilateral triangles = 3(10 - 6) = 3(4) = 12 ft

 

 

Answer 3

e = s -6      4s -3e = 28     4s - 3(s - 6) = 28      4s - 3s + 18 = 28      1s + 18 = 28 Subtract 18 from both sides.

 

1s = 10   4s = 40 perimeter of square.     e = s - 6 = 10 - 6 = 4      3e = 12 perimeter of triangle.