The length of one of the sides of a square was increased by 4 dm, and the other one was decreased by 6 dm. As a result, a rectangle was made with an area of 56 dm2. Find the length of the side of the square

Answer:the length of the side of the square is 10 dm

Step-by-step explanation:

Let x represent the length of each side of the square.

The length of one of the sides of a square was increased by 4 dm, and the other one was decreased by 6 dm. This means that the length of one side of the rectangle formed is (x + 4) dm and the length of the other side of the rectangle is

(x - 6) dm

The are of the rectangle is 56dm². This means that

(x - 6) (x + 4) = 56

x² + 4x - 6x - 24 = 56

x² - 2x - 24 - 56 = 0

x² - 2x - 80 = 0

x² + 8x - 10x - 80 = 0

x (x + 8) - 10 (x + 8) = 0

x - 10 = 0 or x + 8 = 0

x = 10 or x = - 8

Since the length of each side of the square cannot be negative, then

x = 10

The answer to your question is 10 dm

Step-by-step explanation:

Data

length of a rectangle = x + 4

height of a rectangle = x - 6

Area of the rectangle = 56 dm²

length of the square = x

Process

1. - Find x with the information given for the rectangle

Area = length x height

Substitution

56 = (x + 4) (x - 6)

Expand

56 = x² - 2x - 24

Equal to zero

x² - 2x - 24 - 56 = 0

Simplify

x² - 2x - 80 = 0

Factor

(x - 10) (x + 8) = 0

Equal to zero

x₁ - 10 = 0 x₂ + 8 = 0

x₁ = 10 x₂ = - 8

2. - Conclusion

The length of the square is 10 dm because there are no negative lengths.