a=leght of side of original square
b=leght of side of new square
b=a+7
a=b-7
Area of new square is:
A=b^2=121
b=sqroot(121)=11
a=b-7=11-7=4
Length of a side of the original square is 4
b=leght of side of new square
b=a+7
a=b-7
Area of new square is:
A=b^2=121
b=sqroot(121)=11
a=b-7=11-7=4
Length of a side of the original square is 4
Let's assume the original side length of the square is x cm.
According to the given information, when the sides of the square are lengthened by 7cm, the new side length becomes (x + 7) cm. The area of this new square is 121 cm^2.
The formula to find the area of a square is: Area = side length^2.
Using this formula, we can write the equation:
(x + 7)^2 = 121
To solve this equation, we can expand the equation:
x^2 + 2*7*x + 7^2 = 121
Simplifying further:
x^2 + 14x + 49 = 121
Rearranging the equation:
x^2 + 14x + 49 - 121 = 0
x^2 + 14x - 72 = 0
Now, we can solve this quadratic equation using factorization or the quadratic formula.
By factoring, we can rewrite the equation as:
(x + 18)(x - 4) = 0
Setting each factor equal to zero:
x + 18 = 0 or x - 4 = 0
Solving each equation:
x = -18 or x = 4
Since the length of a side cannot be negative, we discard the solution x = -18.
Therefore, the length of a side of the original square is 4 cm.
So, the original square had a side length of 4 cm.