Question

A rectangle with an area of 312 square centimeters has a length and width in a ratio of 13:6. What are the length and width?

length = centimeters

width = centimeter

Answer 1

To find the dimensions of the rectangle, we can start by using the relationship given by the ratio of length to width. Let:

- Length = \( 13x \)
- Width = \( 6x \)

where \( x \) is a common factor.

The area of a rectangle is given by the formula:

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

Substituting the expressions for length and width:

\[
312 = (13x)(6x)
\]

This simplifies to:

\[
312 = 78x^2
\]

To solve for \( x^2 \), divide both sides by 78:

\[
x^2 = \frac{312}{78}
\]

Calculating the right side gives:

\[
x^2 = 4
\]

Taking the square root of both sides:

\[
x = 2
\]

Now, we can find the length and width:
- Length: \( 13x = 13 \times 2 = 26 \) centimeters
- Width: \( 6x = 6 \times 2 = 12 \) centimeters

Thus, the dimensions of the rectangle are:

- Length = 26 centimeters
- Width = 12 centimeters