Gab is an architect who plans to build his own house. He bought a lot measuring 400 square meters. Let (x) represent the width of his lot in meters, express the length of the lot (L) as a function of width x. If the width of the Lot is 15 meters, what is the length of the lot?

Gab's lot measures 400 square meters in total, and we know the area of a rectangle is given by the formula:

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

Let the width be represented by \( x \) and the length be \( L \). The equation for the area becomes:

\[
L \times x = 400
\]

To express the length \( L \) as a function of the width \( x \), solve for \( L \):

\[
L = \frac{400}{x}
\]

This is the expression for the length of the lot as a function of the width \( x \).

Now, if the width of the lot is 15 meters, substitute \( x = 15 \) into the equation:

\[
L = \frac{400}{15} = 26.67 \, \text{meters} 
\]

Thus, if the width of the lot is 15 meters, the length of the lot is approximately 26.67 meters.

Would you like more details on how this equation works or have any other questions?

Here are 5 related questions for further exploration:
1. What would the length be if the width were 10 meters?
2. If Gab decided to change the area of the lot to 500 square meters, how would that affect the length?
3. How does the length change as the width increases?
4. Could you express the width as a function of the length instead?
5. What would happen if Gab divided the lot into two equal rectangular sections?

**Tip:** Always verify the dimensions of your lot using real-world measurements to ensure accuracy during construction planning.

Discover how to calculate the length of a rectangular lot with a total area of 400 square meters by expressing the length as a function of the width. If the width is 15 meters, find out that the length will be approximately 26.67 meters. This problem is ideal for students in Grades 6-8 and introduces key concepts in geometry and algebra.

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