## 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

Question

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

in progress 0
2 weeks 2021-11-15T12:59:56+00:00 2 Answers 0 views 0

1. 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

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.