SOLUTION: two squares have sides x cm and(x+4)cm .the sum of their areas is 656 sq.cm. express this as an algebraic equation in x and solve the equation to find the sides of the squares

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Question 761792: two squares have sides x cm and(x+4)cm .the sum of their areas is 656 sq.cm. express this as an algebraic equation in x and solve the equation to find the sides of the squares
Found 2 solutions by ramkikk66, josmiceli:
Answer by ramkikk66(644) (Show Source):
You can put this solution on YOUR website!
Area of 1st square =
Area of 2nd square =
Sum of areas =
Simplifying and subtracting 656 from both sides

Dividing by 2

This is a standard quadratic equation of the form ax^2 + bx + c = 0 with a = 1, b = 4 and c = -320.
Solving it using the quadratic solver (see below), we get the values of x as
or
Since x cannot be negative, x = 16
So, side of 1st square = and side of second square =
Sum of areas = . Check!
:)

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1296 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 16, -20. Here's your graph:

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The square with side = cm
has area cm2
------------------------
The square with side = cm
has area cm2
-------------------------------
given:

Let

cm2

( This is the equation )
I can complete the square

( There is also a solution , but ignore it )

The sides are 16 cm and 20 cm
check:

OK