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

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

RELATED QUESTIONS
Two squares have sides p cm and (p+5) cms. The sum of their squares is 625 sq.cm. The... (answered by ewatrrr)
A triangle has sides measuring 5 cm, 5 cm and 6 cm. A second triangle is drawn with... (answered by josmiceli)
A triangle has sides measuring 13 cm, 13 cm, and 10 cm. A second triangle is drawn with... (answered by Alan3354)
If the area of an isosceles triangle is x sq. cm and each of the congruent sides measures (answered by KMST)
The sides of a rectangle are x cm and 5 cm. The perimeter is 29 cm. Write an equation... (answered by zhagi17)
Two squares have sides of lengths x cm and( 2x + l) cm. The sum of the perimeters of the... (answered by stanbon)
Two rectangles A and B each have an area of 11 cm^2 The length of rectangle A is x cm... (answered by josmiceli,ikleyn,MathTherapy)
"The base of a triangle is x cm long and its altitude is quarter the length of its base.... (answered by MathLover1)
The sides of an equilateral triangle measure (x+y+3) cm, (3y-2) cm and (2x+y) cm.... (answered by ewatrrr)