Question

The area of the rectangle to the right is 68 square feet

Find the value of x. Length is x+4 and the width is x-9

Answer 1

The value of x in the given rectangle is 13 feet.

Step-by-step explanation:

The area of a rectangle is given by the formula Area = Length × Width. In this case, we know that the area of the rectangle is 68 square feet and the length is x + 4 and the width is x - 9. Substituting these values into the formula, we get:

68 = (x + 4) × (x - 9)

Expanding the equation, we have:

68 = x² - 5x - 36

Now, rearranging the equation to form a quadratic equation:

x² - 5x - 104 = 0

Using the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

Substituting the values into the formula and simplifying, we get two possible values for x: x = 13 or x = -8.

However, since the dimensions of a rectangle cannot be negative, the only valid solution is x = 13.

Therefore, the value of x is 13 feet.

Answer 2

x = 13 feet

Step-by-step explanation:

(x +4) ( x - 9) = x² - 9x + 4x - 36 = x² - 5x - 36.

x² - 5x - 36 is the area. 68 is also the area.

so x² - 5x - 36 = 68

x² - 5x - 36 - 68 = 0

x² - 5x - 104 = 0

(x - 13) (x + 8) = 0

x = 13 or x = -8

x has to be positive, since length of x + 4 = -8 + 4 = -4. cannot have negative length.

so x = 13 feet