If the sides of a square are increased by 3 cm, its area becomes 100 cm2. Find the length of the sides of the original square.
Let's denote the original length of the sides of the square as "x" cm.
We are given that if the sides of the square are increased by 3 cm, its area becomes 100 cm².
The new length of the sides of the square would be (x + 3) cm.
The new area of the square can be calculated using the formula: area = side².
Therefore, the new area is (x + 3)² cm².
According to the question, the new area is given as 100 cm².
So, we can write the equation: (x + 3)² = 100
Expanding the equation, we get: x² + 6x + 9 = 100
Subtracting 100 from both sides, we have: x² + 6x - 91 = 0
To solve this quadratic equation, we can either factorize it or use the quadratic formula.
Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
In this equation, for the quadratic equation ax² + bx + c = 0,
a = 1, b = 6, and c = -91.
Plugging in the values into the quadratic formula, we get:
x = (-6 ± √(6² - 4 * 1 * -91)) / (2 * 1)
x = (-6 ± √(36 + 364)) / 2
x = (-6 ± √400) / 2
x = (-6 ± 20) / 2
Now, solving for both values of x:
x₁ = (-6 + 20) / 2 = 14 / 2 = 7
x₂ = (-6 - 20) / 2 = -26 / 2 = -13
Since side length cannot be negative, we discard the value of -13.
Therefore, the length of the sides of the original square is 7 cm.
To find the length of the sides of the original square, we can follow these steps:
Step 1: Let's assume the length of the sides of the original square is "x" cm.
Step 2: The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side.
Step 3: We are given that when the sides of the square are increased by 3 cm, the new area is 100 cm^2. So, the new length of the sides would be (x + 3) cm.
Step 4: Using the given information, we can create an equation to solve for x:
(x + 3)^2 = 100
Step 5: First, we need to expand the equation:
x^2 + 6x + 9 = 100
Step 6: Rearranging the equation by moving 100 to the other side:
x^2 + 6x + 9 - 100 = 0
x^2 + 6x - 91 = 0
Step 7: Now, we can solve this quadratic equation for x. We can either factorize it or use the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/2a
For our equation x^2 + 6x - 91 = 0, a = 1, b = 6, and c = -91.
x = (-6 ± √(6^2 - 4(1)(-91)))/2(1)
x = (-6 ± √(36 + 364))/2
x = (-6 ± √400)/2
x = (-6 ± 20)/2
Step 8: Now we solve the equation:
x = (-6 + 20)/2 = 14/2 = 7
or
x = (-6 - 20)/2 = -26/2 = -13
Since we are dealing with lengths, the negative value doesn't make sense in this context. Therefore, the length of the sides of the original square is 7 cm.
original side = s
new side = s+3
(s+3)^2 = 100
now go for it. Come back if you get stuck.