To determine the dimensions of the rectangle, let's use the information provided:
1. Define the width of the rectangle as [tex]\( w \)[/tex].
2. The length of the rectangle, [tex]\( l \)[/tex], is equal to one more than twice the width:
[tex]\[
l = 2w + 1
\][/tex]
3. The perimeter of a rectangle is given by the formula:
[tex]\[
P = 2l + 2w
\][/tex]
We are told that the perimeter is 89 cm, so:
[tex]\[
2l + 2w = 89
\][/tex]
4. Substitute the expression for [tex]\( l \)[/tex] (from step 2) into the perimeter formula:
[tex]\[
2(2w + 1) + 2w = 89
\][/tex]
5. Simplify the equation by distributing the 2:
[tex]\[
4w + 2 + 2w = 89
\][/tex]
6. Combine like terms:
[tex]\[
6w + 2 = 89
\][/tex]
7. Subtract 2 from both sides to isolate the term with [tex]\( w \)[/tex]:
[tex]\[
6w = 87
\][/tex]
8. Finally, solve for [tex]\( w \)[/tex] by dividing both sides by 6:
[tex]\[
w = \frac{87}{6} = 14.5
\][/tex]
So, the width [tex]\( w \)[/tex] of the rectangle is 14.5 cm.
9. Now, calculate the length [tex]\( l \)[/tex] using the expression [tex]\( l = 2w + 1 \)[/tex]:
[tex]\[
l = 2(14.5) + 1 = 29 + 1 = 30
\][/tex]
Therefore, the length [tex]\( l \)[/tex] of the rectangle is 30 cm.
In conclusion, the dimensions of the rectangle are:
- Width: 14.5 cm
- Length: 30 cm
