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.

Answer 1

Let x be the shorter side of the rectangular house. Since the length of the house is two-and-a-half times its width, we can write this as 2.5x. The area of a rectangle is given by the formula length * width, so the area of the rectangular house in terms of x is 2.5x * x = 2.5x^2. This is the expression for the area of the rectangular house in terms of the shorter side x.

Answer 2

`2.5x^2`

Explanation:

Let x be the shorter side of the rectangle, which is also its width (w), so:

`w=x`

Given that the length of the rectangle is two-and-a-half times its width, this means the length (l) can be expressed as:

`l=2.5x`

The area of a rectangle (A) is the product of its length (l) and width (w):

`A =l \cdot w`

Substitute the expressions for length and width into the formula for area:

`A=2.5x \cdot x`

Simplify this expression:

`A=2.5x^2`

Therefore, the expression for the area of the rectangle in terms of x is:

`\Large\boxed{\boxed{2.5x^2}}`