If the sides of a square are lengthened by 6 cm the area becomes 196 cm 2 find the length of a side of the original square?
Area of a square = s^2 (side squared)
x = side of original square
x + 6 = side of lengthened square
196 = (x + 6)^2
Solve for x.
Let's represent the length of the original side of the square as "x" cm.
According to the given information, if the sides of the square are lengthened by 6 cm, the new side length would be (x + 6) cm.
The area of the new square is given as 196 cm^2. We can calculate this using the formula A = s^2, where A represents the area and s represents the side length of the square.
So, for the new square:
A = (x + 6)^2
We know that A = 196 cm^2, so we can write the equation as:
(x + 6)^2 = 196
Now let's solve for x:
Taking the square root of both sides:
√((x + 6)^2) = √196
(x + 6) = 14
Subtracting 6 from both sides:
x = 14 - 6
x = 8
Therefore, the length of a side of the original square is 8 cm.
To find the length of a side of the original square, we can work backwards from the given information.
Let's assume the length of each side of the original square is 'x' cm.
If the sides of the square are lengthened by 6 cm, the new length of each side would be '(x + 6)' cm.
The area of a square is calculated by multiplying the length of one side by itself. So, the area of the original square would be 'x * x = x^2'.
Similarly, the area of the new square would be '(x + 6) * (x + 6) = (x + 6)^2'.
According to the given information, the new area is 196 cm^2. So, we can set up the equation:
(x + 6)^2 = 196
To solve for x, we can take the square root of both sides:
sqrt((x + 6)^2) = sqrt(196)
Simplifying:
x + 6 = 14
Now, we can solve for x by subtracting 6 from both sides:
x = 14 - 6
x = 8
Therefore, the length of a side of the original square is 8 cm.