Question

The ratio of 2 sides of a parallelogram is 3:4, and the perimeter is 28 in. FInd the lengths of the sides of the parallelogram.

Answer 1

Let the lengths of the sides of the parallelogram be \(3x\) and \(4x\), where \(x\) is a common multiplier.

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

\[
P = 2(\text{length} + \text{width}) = 2(3x + 4x) = 2(7x) = 14x
\]

Given that the perimeter is 28 inches, we can set up the equation:

\[
14x = 28
\]

To find \(x\), divide both sides by 14:

\[
x = \frac{28}{14} = 2
\]

Now we can find the lengths of the sides:

1. Length of the first side:

\[
3x = 3(2) = 6 \text{ inches}
\]

2. Length of the second side:

\[
4x = 4(2) = 8 \text{ inches}
\]

Thus, the lengths of the sides of the parallelogram are 6 inches and 8 inches.