Question
The length of a rectangular house is two and a half times its width. Solve the problem using x to denote the shorter side of the rectangle.
Construct the expression for the area of the rectangle in terms of x.
Construct the expression for the area of the rectangle in terms of x.
Answers
GPT-4o mini
Let \( x \) represent the width (shorter side) of the rectangular house. Given that the length is two and a half times the width, we can express the length as:
\[
\text{Length} = 2.5x = \frac{5}{2}x
\]
The area \( A \) of a rectangle is calculated by multiplying the length by the width:
\[
A = \text{Length} \times \text{Width}
\]
Substituting the expressions for length and width into the area formula, we get:
\[
A = \left(\frac{5}{2}x\right) \times x
\]
This simplifies to:
\[
A = \frac{5}{2}x^2
\]
Thus, the expression for the area of the rectangle in terms of \( x \) is:
\[
A = \frac{5}{2}x^2
\]
\[
\text{Length} = 2.5x = \frac{5}{2}x
\]
The area \( A \) of a rectangle is calculated by multiplying the length by the width:
\[
A = \text{Length} \times \text{Width}
\]
Substituting the expressions for length and width into the area formula, we get:
\[
A = \left(\frac{5}{2}x\right) \times x
\]
This simplifies to:
\[
A = \frac{5}{2}x^2
\]
Thus, the expression for the area of the rectangle in terms of \( x \) is:
\[
A = \frac{5}{2}x^2
\]