Question

If the area of the rectangle below is 39 square feet, find the value of x
On rectangle length x +8 width x-2

Answer 1

To find the value of \( x \) for the rectangle with an area of 39 square feet, we can set up the equation using the formula for the area of a rectangle, which is:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Given that the length is \( x + 8 \) and the width is \( x - 2 \), we can write the equation for the area as follows:

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

Next, we will expand the left-hand side:

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

Combining like terms gives:

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

Now, we will move all terms to one side of the equation:

\[
x^2 + 6x - 16 - 39 = 0
\]

This simplifies to:

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

Now we can factor or use the quadratic formula to solve for \( x \). The equation factors as:

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

Setting each factor equal to zero gives us:

\[
x + 11 = 0 \quad \Rightarrow \quad x = -11
\]

\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]

Since \( x \) represents a dimension of the rectangle, it must be a positive value, so we take \( x = 5 \).

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

\[
\boxed{5}
\]