Question

Consider the reduction of the rectangle.

A large rectangle has a length of 16.8 feet and width of 2.3 feet. A smaller rectangle has a length of 4.5 feet and width of x feet.
Not drawn to scale

Rounded to the nearest tenth, what is the value of x?
0.1 feet
0.6 feet
1.6 feet
2.0 feet

Answer 1

To find the value of \( x \) that maintains the same proportion between the large rectangle and the small rectangle, we can set up a proportion using the given dimensions.

The large rectangle dimensions are:
- Length = 16.8 feet
- Width = 2.3 feet

The smaller rectangle dimensions are:
- Length = 4.5 feet
- Width = \( x \) feet

We will use the ratio of the length and width of both rectangles to find \( x \).

Set up the ratio for the rectangles:

\[
\frac{\text{Length of large rectangle}}{\text{Width of large rectangle}} = \frac{\text{Length of small rectangle}}{\text{Width of small rectangle}}
\]

Inserting the values gives us:

\[
\frac{16.8}{2.3} = \frac{4.5}{x}
\]

Now, we can cross-multiply to solve for \( x \):

\[
16.8 \cdot x = 2.3 \cdot 4.5
\]

Calculate \( 2.3 \cdot 4.5 \):

\[
2.3 \cdot 4.5 = 10.35
\]

So, the equation becomes:

\[
16.8x = 10.35
\]

Now, divide both sides by 16.8 to isolate \( x \):

\[
x = \frac{10.35}{16.8}
\]

Calculating this gives:

\[
x \approx 0.61607
\]

Rounding this to the nearest tenth results in:

\[
x \approx 0.6
\]

Thus, the value of \( x \) rounded to the nearest tenth is:

\[
\boxed{0.6 \text{ feet}}
\]