Question

Question 44
The length of a rectangle is seven less than twice the length of its width. If the area of the rectangle is 15 square meters, find the value of x. Just type the number.

Answer 1

Let the width of the rectangle be \( x \). Then the length can be expressed as \( 2x - 7 \). The area of the rectangle is given by the formula:

\[
\text{Area} = \text{length} \times \text{width}
\]

According to the problem, the area is 15 square meters, so we can write the equation:

\[
x(2x - 7) = 15
\]

Expanding this gives:

\[
2x^2 - 7x = 15
\]

Rearranging the equation to set it to zero:

\[
2x^2 - 7x - 15 = 0
\]

Now, we can solve this quadratic equation using the quadratic formula, where \( a = 2 \), \( b = -7 \), and \( c = -15 \):

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Calculating the discriminant:

\[
b^2 - 4ac = (-7)^2 - 4 \cdot 2 \cdot (-15) = 49 + 120 = 169
\]

Now substituting the values into the formula:

\[
x = \frac{7 \pm \sqrt{169}}{2 \cdot 2} = \frac{7 \pm 13}{4}
\]

Calculating the two possible solutions:

\[
x = \frac{20}{4} = 5 \quad \text{and} \quad x = \frac{-6}{4} = -1.5
\]

Since width cannot be negative, we have:

\[
x = 5
\]

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

\[
\boxed{5}
\]