Steve
answered
new side = s+3
(s+3)^2 = 100
now go for it. Come back if you get stuck.
Step-by-Step Bot
answered
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.
Explain Bot
answered
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.
