The total area of two square windows is 1,025^2 in.2. Each side of the larger window is 5 in. longer than the sides of the smaller window. How long are the sides of the smaller window?
a.13.5 in.
b.20 in.
c.25 in.
d.31.6 in.
Please help me and explain
I'm not asking for answers...
To find the length of the sides of the smaller window, we can set up a system of equations based on the given information.
Let's assume that the smaller window has a side length of "x" inches.
We know that the total area of the two square windows is 1,025^2 square inches. The area of a square can be found by squaring the length of one of its sides. So, the area of the smaller window would be x^2 in^2.
The larger window has sides that are 5 inches longer than the sides of the smaller window. Therefore, the sides of the larger window would be (x+5) inches.
The total area of the two windows is given as 1,025^2 in^2. This means that the sum of their areas must be equal to 1,025^2.
So, we can set up the following equation:
x^2 + (x+5)^2 = 1,025^2
Now, we can solve this equation to find the value of x, which represents the length of the sides of the smaller window.
x^2 + (x+5)^2 = 1,025^2
Simplifying,
x^2 + (x^2 + 10x + 25) = 1,050,625
Combining like terms,
2x^2 + 10x + 25 = 1,050,625
Rearranging,
2x^2 + 10x + 25 - 1,050,625 = 0
2x^2 + 10x - 1,050,600 = 0
Now we have a quadratic equation. We can solve it using factoring, completing the square, or the quadratic formula.
By using the quadratic formula, the general formula for solving a quadratic equation ax^2 + bx + c = 0 is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, the coefficients of the quadratic equation are a = 2, b = 10, and c = -1,050,600.
Applying the quadratic formula:
x = (-10 ± sqrt(10^2 - 4(2)(-1,050,600))) / 2(2)
Simplifying,
x = (-10 ± sqrt(100 - (-8,402,400))) / 4
x = (-10 ± sqrt(8,402,500)) / 4
Since we are only interested in the positive value for the length of the sides, we can ignore the negative solution.
Taking the positive square root,
x = (-10 + sqrt(8,402,500)) / 4
Calculating the square root,
x ≈ (-10 + 2,894.23) / 4
x ≈ 2,884.23 / 4
x ≈ 721.06
Therefore, the length of the sides of the smaller window is approximately 721.06 inches.
However, from the answer choices provided, the lengths seem to be given in whole numbers. Thus, it seems that there may be an error in the problem statement or the answer choices.
uyioyuio
yuh
let smaller window be x by x
let the larger window be (x+5) by (x+5)
so: x^2 + (x+5)^2 = 1025
expand and solve the quadratic