The sides of two squares differ by 25cm while the sum of their areas is 2425cm. What is the length of the side of each square.

Please answer. Thank you

sides: x and x+25

areas: x^2 and (x+25)^2

now finish it off.

Sir, I know the answer--45&20

45-20=25
(45)^2+(20)^2=2425
(2025)+(400)=2425

but I don't know how to solve in step by step..

Can I get the solution.. Thank you

To solve this problem, we can set up two equations based on the given information.

Let's assume that the side length of one square is "x" cm. Therefore, the side length of the other square would be "x + 25" cm, as the sides of the two squares differ by 25 cm.

The area of a square is given by multiplying the side length by itself. So, the equation for the sum of their areas can be written as:

x^2 + (x + 25)^2 = 2425

Now, we can solve this equation to find the value of x, which represents the side length of one square.

Expanding and simplifying the equation:
x^2 + (x^2 + 50x + 625) = 2425
2x^2 + 50x + 625 = 2425
2x^2 + 50x - 1800 = 0

Next, we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

2(x^2 + 25x - 900) = 0

Now we have a simpler quadratic equation:

x^2 + 25x - 900 = 0

We can factor this equation as:

(x + 45)(x - 20) = 0

Setting each factor equal to 0:

x + 45 = 0 or x - 20 = 0
x = -45 or x = 20

Since the side length of a square cannot be negative, we discard the negative value and conclude that the side length of one square is 20 cm.

Therefore, the side length of the other square is x + 25 = 20 + 25 = 45 cm.

Thus, the length of the sides of the two squares are 20 cm and 45 cm, respectively.