Word problem?

Question

Any help?

If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm^2. What are the dimensions of the original square?

Answer 1

Let x be the side of the squre (b/c I started before using a different variable)

x^2-(x-2)^2=36
Your starting equation. The difference in area between the two squares

x^2-X^2+4x-4=36
Multiply out. Make sure you get the signs correct in the final expression.

4x-4=36 Subtract the common terms

x=10 two steps in one.

Answer 2

Ok, the thing to know about answering a word problem is to figure out how to express it in math terms. This usually starts by writing down what you know, and figure out how its all related. In this case, the important bits to know/pick out are:

1) Area for squares is figured by multiplying the length of one side times the length of the other side. Since its a square, these two sides are the same and you can represent this as Side x Side, or in math terms, Side ^2 (side squared)
2) You are talking about 2 squares
3) the relationship of the sides of the two squares is (SmallSide = BigSide -2)
4) The relationship of the areas is a difference (minus) of 36.

So you write down:
Y = length of bigger square side (The original square)
AreaY = Area of bigger square = Y x Y
Z = length of smaller square side = Y - 2 (IMPORTANT PART)
AreaZ = Area of smaller square = Z x Z

Since you know the areas are different by 36, you can create the relationship:
AreaY - AreaZ = 36 (IMPORTANT PART)
Substituting more variables,
(Y x Y) - (Z x Z) = 36

Finally, since you know the relationship between the two sides
Z= Y - 2, you substitute that in:
(Y x Y) - (Y-2 x Y-2) = 36
(Y^2) - (Y^2 -2Y - 2Y +4 ) = 36
Y^2 - Y^2 + 4Y - 4 = 36
4Y = 36 + 4
4Y = 40
Y = 10

Double check it by putting it back into the equation and seeing if it makes sense...

10 x 10 = 100
(10-2) x (10-2) = 64
100 - 64 = 36

Tada!