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how to make a word problem into a equation

The side of an equilateral triangle is 2 inches shorter than the side of a
square. The perimeter of the square is 30 inches more than the perimeter
of the triangle. Find the length of a side of the triangle.

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2 Answers

Hi, Mercedes.

The key to figuring this one out is to draw your two shapes.  

Since all three sides of an equilateral triangle have the same measure, label all three sides with an x.
Since all four sides of a square have the same measure, we will label them with the same expression as each other: x + 2.  The reason the expression is x + 2 is because the triangle's sides are two inches shorter than the rectangle's sides (so the rectangle's sides are two inches longer).

Now address Perimeter.  To find the perimeter, add the sides together.
Triangle: x + x + x = 3x
Square:  (x + 2) + (x + 2) + (x + 2) + (x + 2) = 4(x + 2) or 4x + 8

The Perimeter of the square is 30 inches more than the Perimeter of the triangle.

P (square) = P (triangle) + 30
4x + 8 = 3x + 30

This should help in setting up your equation.

*Note - you could have labeled the triangle's sides with (x - 2) and the square's sides with x.  
In that case, your equation would be: 4x = 3(x - 2) + 30.  
Either way will work. 

Hi Mercedes!  Try to write down what you know...  

First, name things with single letters.  For example, let's name each side of the square as "s", and each side of the triangle as "t" (easy to remember t=triangle and s=square :-)

Now translate "side of an equilateral triangle is 2 inches shorter than the side of a square":

t = s-2  (triangle side t is 2" less than square side s)

And, "perimeter of the square is 30 inches more than the perimeter of the triangle":

Perimeter of a square = 4s (add all 4 sides together, and since all sides are the same, = 4s)

Perimeter of a triangle = 3t (add all 3 sides together, and since all sides are the same, = 3t)

So now we have 4s = 3t + 30 (square perimeter is 30" longer than triangle perimeter)

We have two unknowns, s and t.  But we also have two equations (in bold, above).  So we fix that by substituting one unknown with its counterpart using the other unknown:

into 4s = 3t + 30, we can substitute  T = s - 2, so 4s = 3(s-2) + 30;  4s = 3s - 6 + 30,

so 4s - 3s = 3s - 3s + 30 - 6, or s = 24

Now put that 24 back into t = s - 2; t = 24 - 2;   t = 22.

 

Let's check, is that correct?

triangle side of 22 is 2" shorter than the square side of 24 - check.

The triangle perimeter = 3t = 3(22) = 66, and the square perimeter = 4s = 4(24) = 96;  96 - 66 = 30 - check.