Question

A rectangle's length and width are in a ratio of 3:2. The perimeter is 100 meters. What are the length and width?

length =
meters

width =
meters

Answer 1

Let the length of the rectangle be \( L \) and the width be \( W \). According to the problem, the length and width are in a ratio of 3:2, which we can express as:

\[
L = 3x \quad \text{and} \quad W = 2x
\]

for some variable \( x \).

The formula for the perimeter \( P \) of a rectangle is given by:

\[
P = 2L + 2W
\]

We know the perimeter is 100 meters, so we can set up the equation:

\[
2L + 2W = 100
\]

Substituting the expressions for \( L \) and \( W \):

\[
2(3x) + 2(2x) = 100
\]

Simplifying this:

\[
6x + 4x = 100
\]

\[
10x = 100
\]

Now, we solve for \( x \):

\[
x = 10
\]

Now we can find the length and width:

\[
L = 3x = 3(10) = 30 \text{ meters}
\]
\[
W = 2x = 2(10) = 20 \text{ meters}
\]

Finally, the dimensions of the rectangle are:

\[
\text{length} = 30 \text{ meters}
\]
\[
\text{width} = 20 \text{ meters}
\]