if the sides of a square are increased by 5 cm the area of the new square is four times the area of the original square. Find the length of a side of the original square.
Let x = side of square.
(x+5)^2 = 4x^2
Solve for x.
To solve this problem, we can start by assigning a variable to represent the length of a side of the original square.
Let's say the length of a side of the original square is 'x' cm.
According to the problem, if the sides of the square are increased by 5 cm, the new square would have sides measuring (x + 5) cm.
We are also given that the area of the new square is four times the area of the original square.
The area of a square is calculated by squaring the length of one side. Therefore, the area of the original square is x^2 square cm, and the area of the new square is (x + 5)^2 square cm.
According to the problem, we have the equation:
(x + 5)^2 = 4(x^2)
Now, let's solve the equation to find the value of 'x'.
Expanding the left side of the equation, we have:
x^2 + 10x + 25 = 4x^2
Rearranging the equation in standard quadratic form:
4x^2 - x^2 - 10x - 25 = 0
Combining like terms:
3x^2 - 10x - 25 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, the equation cannot be easily factored, so we will use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 3, b = -10, and c = -25. Substituting these values into the quadratic formula:
x = (-(-10) ± √((-10)^2 - 4*3*(-25))) / (2*3)
Simplifying:
x = (10 ± √(100 + 300)) / 6
x = (10 ± √400) / 6
x = (10 ± 20) / 6
Now we have two possible solutions:
x = (10 + 20) / 6 = 30 / 6 = 5
x = (10 - 20) / 6 = -10 / 6 = -5/3
Since the length of a side of a square cannot be negative, we can disregard the second solution.
Therefore, the length of a side of the original square is 5 cm.