Question

Question 42
If the area of the rectangle below is 39 square feet, find the value of x. Just type the number.
x-2
x+8

Answer 1

To find the value of \( x \) for the rectangle with dimensions \( (x - 2) \) and \( (x + 8) \) and an area of 39 square feet, we can set up the equation:

\[
(x - 2)(x + 8) = 39
\]

Expanding the left side:

\[
x^2 + 8x - 2x - 16 = 39
\]

Simplifying, we have:

\[
x^2 + 6x - 16 = 39
\]

Subtracting 39 from both sides:

\[
x^2 + 6x - 55 = 0
\]

Now, we can factor the quadratic equation:

\[
(x + 11)(x - 5) = 0
\]

Setting each factor to zero gives us:

\[
x + 11 = 0 \quad \text{or} \quad x - 5 = 0
\]

From \( x + 11 = 0 \):

\[
x = -11 \quad (\text{not valid since length cannot be negative})
\]

From \( x - 5 = 0 \):

\[
x = 5
\]

Thus, the value of \( x \) is:

\[
\boxed{5}
\]