If the sides of a square are lengthened by 8 cm, the area becomes 256cm^2. Find the length of a side of the original square.
original square : x by x
new square : (x+8) by (x+8)
so (x+8)^2 = 256
x+8 = √256 = 16
x= 8
original square was 8 by 8
check: new square is 16 by 16 or 256
The square root of 256 is 16. Therefore the original square has side lengths of 8.
To find the length of a side of the original square, we can use the information given and set up an equation.
Let's say the original length of a side of the square is 'x' cm. When the sides are lengthened by 8 cm, the new length becomes 'x + 8' cm.
We know that the area of a square is equal to the square of its side length. Therefore, the area of the original square is 'x^2' cm^2, and the area of the new square is '(x + 8)^2' cm^2.
According to the given information, the area of the new square is 256 cm^2. So, we can set up the equation:
(x + 8)^2 = 256
To solve this equation, we can take the square root of both sides:
√((x + 8)^2) = √256
Simplifying,
x + 8 = 16
Now, we can isolate 'x' by subtracting 8 from both sides:
x = 16 - 8
x = 8
Therefore, the length of a side of the original square is 8 cm.