Respuesta :

alexanderorangeguy

Answer:

17, 5

Step-by-step explanation:

Let the width be x

width = x

length = x + 12

length x width = x(x + 12)

length x width = x² + 12x

x² + 12x = 85

x² + 12x - 85 = 0

Now it is just a quadratic:

The 2 numbers we need are 17 and -5

(x + 17)(x - 5) = 0

x = -17 or x = 5.

Since width and length cannot be negative, x must equal 5.

Width = 5

length = 17

The answer is 17, 5.

We are given two things :

  1. Length exceeds width by 12 inches
  2. Area = 85 square inches

We can represent the length and width as x + 12 and x respectively.

Now, the formula for the area of a rectangle is :

Area = Length x width

Now, let's substitute the values for length and width in the formula along with the area.

  • (x + 12)(x) = 85
  • x² + 12x = 85
  • x² + 12x - 85 = 0

We now have a quadratic equation, which can either be solved by splitting the middle term, or by using the quadratic formula. For convenience purposes, we'll go with the first one.

  • x² + 17x - 5x - 85 = 0
  • x (x + 17) - 5 (x + 17) = 0
  • (x + 17)(x - 5) = 0
  • x = 17, 5

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