Answer:
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.
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
