If the sides of a square are lengthened by 7cm, the area becomes 121cm2. Find the length of a side of the original square.
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
To solve this problem, we can use the concept of areas of squares and the relationship between the side length and the area.
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.