If the sides of of a square are decreased by 2cm, the area is decreased by 36cm square. What are the dimensions of the original square?
original square: x by x
new square: x-2 by x-2
old area = x^2
new area = (x-2)^2
The difference in these area = 36
difference means subtract.
take it from there.
10
To solve this problem, we can set up an equation based on the given information. Let's assume the original square has side length "x" cm.
The area of the original square is given by x^2 square cm.
Now, according to the problem, if the sides of the square are decreased by 2 cm, the new square has side length (x-2) cm.
The area of the new square is given by (x-2)^2 square cm.
The problem states that the area of the original square is decreased by 36 cm^2.
So, we can set up the following equation:
x^2 - (x-2)^2 = 36
To solve this equation, we can expand the square term and simplify:
x^2 - (x^2 - 4x + 4) = 36
Next, distribute the negative sign:
x^2 - x^2 + 4x - 4 = 36
Combine like terms:
4x - 4 = 36
Add 4 to both sides:
4x - 4 + 4 = 36 + 4
Simplify:
4x = 40
Divide both sides by 4:
4x/4 = 40/4
Simplify:
x = 10
Therefore, the original square has dimensions of 10 cm by 10 cm.