Question

Use the image to answer the question.

An illustration shows a rectangle upper A upper B upper C upper D formed by joining four points. Side upper A upper B is labeled as 3 x and is parallel to upper C upper D. Side upper A upper D is labeled as 5 x and is parallel to upper B upper C.

Find the longer side of the rectangle shown, which has a perimeter of 64 cm.

(1 point)
Responses

40 cm
40 cm

4 cm
4 cm

12 cm
12 cm

20 cm

Answer 1

To find the longer side of the rectangle, we can use the information given regarding the perimeter of the rectangle and the lengths of the sides.

The perimeter \(P\) of a rectangle is calculated using the formula:

\[
P = 2 \times (\text{length} + \text{width})
\]

From the illustration, we have:

- One side (length) labeled as \(3x\)
- The other side (width) labeled as \(5x\)

Given that the perimeter of the rectangle is 64 cm, we can set up the equation:

\[
2 \times (3x + 5x) = 64
\]

Simplifying this:

\[
2 \times (8x) = 64
\]

\[
16x = 64
\]

Now, solving for \(x\):

\[
x = \frac{64}{16} = 4
\]

Now we can find the actual lengths of the sides:

- Length (\(3x\)) = \(3 \times 4 = 12\) cm
- Width (\(5x\)) = \(5 \times 4 = 20\) cm

The longer side of the rectangle is:

\[
\text{Width} = 20 \text{ cm}
\]

Therefore, the longer side of the rectangle is **20 cm**.