An area, A, consisting of the sum of two squares is 1000. The side of one square is 10 less than 2/3 of the side of the other square. What are the sides of the squares?

Let x,y be the side of each of the squares.

x2 + y2 = 1000
y=(2/3)x-10

substitute (2/3)x-10 for y in the first equation:
x2 + ((2/3)x-10)2 = 1000

Expand and solve for the quadratic equation to get x=30 or x=-270/13.
Reject second solution to get x=30, y=10

See also
http://www.jiskha.com/display.cgi?id=1246414274

To find the sides of the squares, we can set up a system of equations based on the given information.

Let's assume the side of one square is "x" and the side of the other square is "y".

According to the problem, the area (A) consisting of the sum of two squares is 1000. The area of a square is given by the formula A = side^2.

So, we have the equation:

x^2 + y^2 = 1000 -- Equation 1

It is also given that the side of one square is 10 less than 2/3 of the side of the other square.

Mathematically, this can be represented as:

x = (2/3)y - 10

Simplifying the equation, we have:

3x = 2y - 30 -- Equation 2

Now, we have a system of equations:
x^2 + y^2 = 1000 -- Equation 1
3x = 2y - 30 -- Equation 2

To solve this system, we can use substitution or elimination methods.

Let's use substitution method:
From Equation 2, we can rewrite it as:
3x - 2y = -30

Solving for "x", we have:
3x = 2y - 30
x = (2y - 30)/3

Now, substitute the value of "x" in Equation 1:
((2y - 30)/3)^2 + y^2 = 1000

Simplifying the equation further, we have:
4y^2 - 120y + 900 + 9y^2 = 3000

Combining like terms, we get:
13y^2 - 120y - 2100 = 0

Now, we can solve this quadratic equation for "y" using factoring, completing the square, or the quadratic formula.

Once we find the value of "y", we can substitute it back into Equation 2 to find the value of "x".

As a result, we will have the values for the sides of the two squares.