To solve this problem, we need to follow these steps:
1. Understand the given relationships:
- The length (L) of the rectangle is 4 centimeters less than twice its width (W).
- The perimeter (P) of the rectangle is 34 cm.
2. Express the length in terms of the width using the given relationship:
[tex]\[
\text{Length} = 2 \times \text{Width} - 4
\][/tex]
So,
[tex]\[
L = 2W - 4
\][/tex]
3. Use the formula for the perimeter of a rectangle, which is:
[tex]\[
P = 2 \times (\text{Length} + \text{Width})
\][/tex]
Given that the perimeter is 34 cm, we can set up the equation:
[tex]\[
34 = 2 \times (L + W)
\][/tex]
4. Substitute the expression for L from step 2 into the perimeter equation:
[tex]\[
34 = 2 \times ((2W - 4) + W)
\][/tex]
5. Simplify and solve for width (W):
[tex]\[
34 = 2 \times (3W - 4)
\][/tex]
[tex]\[
34 = 6W - 8
\][/tex]
[tex]\[
42 = 6W
\][/tex]
[tex]\[
W = 7
\][/tex]
6. Once we have the width (W), we can find the length (L) using the relationship from step 2:
[tex]\[
L = 2W - 4
\][/tex]
[tex]\[
L = 2 \times 7 - 4
\][/tex]
[tex]\[
L = 14 - 4
\][/tex]
[tex]\[
L = 10
\][/tex]
Therefore, the dimensions of the rectangle are:
- Length: 10 cm
- Width: 7 cm
Among the provided options, the correct one is:
- Length: 10 cm, Width: 7 cm
