Respuesta :

mathstudent55
A = LW

LW = A

(x + 3)(x - 8) = 42

x^2 - 8x + 3x - 24 = 42

x^2 - 5x - 66 = 0

(x - 11)(x + 6) = 0

x - 11 = 0    or    x + 6 = 0

x = 11         or    x = -6

The length of the side of a rectangle cannot be a negative number, so we discard the negative answer, x = -6.

Answer: x = 11
Lanuel

Since the area of this rectangle is 42 inches, the value of x is equal to 11 inches.

Given the following data:

  • Length of rectangle = (x - 8) inches.
  • Width of rectangle = (x + 3) inches.
  • Area of rectangle = 42 inches.

How to calculate the area?

Mathematically, the area of a rectangle is calculated by using this formula:

A = LW

Where:

  • L is the length.
  • W is the width.

Substituting the given parameters into the formula, we have;

42 = (x - 8)(x + 3)

42 = x² + 3x - 8x - 24

42 = x² - 5x - 24

x² - 5x - 24 - 42 = 0

x² - 5x - 66 = 0

Solving the quadratic equation by factorization, we have:

x² - 11x + 6x - 66 = 0

x(x - 11) + 6(x - 11) = 0

(x + 6)(x - 11) = 0

x = -6 or x = 11.

Note: The dimensions of a rectangle cannot be negative.

Therefore, x = 11 inches.

Read more on rectangle here: https://brainly.com/question/25292087

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