A square has sides 5cm smaller than the sides of a second square. The ...
Given,
(Area)B = 4 × (Area)A
⇒ x
2 = 4(x – 5)
2⇒ x
2 = 4[x
2 + 25 – 10x]
⇒ x
2 = 4x
2 + 100 – 40x
⇒ 3x
2 – 40x + 100 = 0
⇒ 3x
2 – 30x – 10x + 100 = 0
⇒ 3x(x – 10) – 10(x – 10) = 0
⇒ x = 10
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A square has sides 5cm smaller than the sides of a second square. The ...
To solve this problem, let's assume that the side length of the smaller square is x cm.
1. Finding the area of the smaller square:
The area of a square is given by the formula A = side^2. Therefore, the area of the smaller square is x^2.
2. Finding the side length of the larger square:
According to the problem, the side length of the larger square is 5 cm longer than the side length of the smaller square. So, the side length of the larger square is (x + 5) cm.
3. Finding the area of the larger square:
The area of the larger square is four times the area of the smaller square. So, we have the equation 4(x^2) = (x + 5)^2.
4. Solving the equation:
Expanding the right side of the equation, we get 4x^2 = x^2 + 10x + 25.
Rearranging the terms, we have 3x^2 - 10x - 25 = 0.
5. Solving the quadratic equation:
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 3, b = -10, and c = -25.
Calculating the discriminant (b^2 - 4ac), we get:
b^2 - 4ac = (-10)^2 - 4(3)(-25) = 100 + 300 = 400.
Since the discriminant is positive, we have two real solutions:
x = (-(-10) ± √400) / (2(3))
x = (10 ± 20) / 6
6. Determining the side length of the larger square:
Since the side length of a square cannot be negative, we discard the negative solution and consider the positive solution:
x = (10 + 20) / 6 = 30 / 6 = 5 cm.
Therefore, the side length of the larger square is 5 cm + 5 cm = 10 cm.
7. Finding the correct answer:
The question asks for the side length of the larger square in centimeters. From our calculations, we determined that the side length of the larger square is 10 cm. Therefore, the correct answer is option C) 10.00 cm.
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