Answer:
D
Explanation:
The perimeter of a rectangle is given by the formula:
![P=2(l+w)](https://img.qammunity.org/2021/formulas/mathematics/high-school/u2zh6atmobu8pylyyhrjk8f41mol6cwppd.png)
From our figure, our length is (2s-5) and our width is (4s-13). So, let's substitute (2s-5) for l and (4s-13) for w. This yields:
![P=2((2s-5)+(4s-13))](https://img.qammunity.org/2021/formulas/mathematics/college/czojhomc1ct5z07l93fkvh0h56he0iwf61.png)
We also know that the perimeter is 108. So, substitute that for P:
![108=2(2s-5+4s-13)](https://img.qammunity.org/2021/formulas/mathematics/college/wxhr56vtfxldng3o4rukb2mngqetstugap.png)
Solve for s. We can first divide everything by 2:
![54=2s-5+4s-13](https://img.qammunity.org/2021/formulas/mathematics/college/nnbic5r7flflndbh7lwf3wyibhhsgdbkn3.png)
Combine like terms:
![54=(2s+4s)+(-5-13)](https://img.qammunity.org/2021/formulas/mathematics/college/1p081ns0iofeszrww1fu3wd7oreqcx5dqk.png)
Add or subtract:
![54=6s-18](https://img.qammunity.org/2021/formulas/mathematics/college/cilhmwsc0zxgmfspmw5fls58hhg5xpal7w.png)
Add 18 to both sides:
![72=6s](https://img.qammunity.org/2021/formulas/mathematics/college/94g7bdgbyswxeyhvpymeiqyjg92v5r9oz9.png)
Divide both sides by 6:
![s=12](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ihntui043sfgfw55cjc9i0kuf4ki8v1m2v.png)
So, the value of s is 12.
Now, substitute this back in to find our length and width:
![l=2s-5](https://img.qammunity.org/2021/formulas/mathematics/college/15tjf65691o962tv9kqvhwwg1jg1uwdd0s.png)
Substitute 12 for s:
![l=12(2)-5](https://img.qammunity.org/2021/formulas/mathematics/college/gk685tto3ljzhw5eep1tb2g53f9ksmrpdj.png)
Multiply and subtract:
![l=24-5=19](https://img.qammunity.org/2021/formulas/mathematics/college/9amc2m7shlv93c6xiheo4ps306o8n3scug.png)
Now, let's find the width:
![w=4s-13](https://img.qammunity.org/2021/formulas/mathematics/college/hwd00yxewywc68o4usw0ji82g2y4axqorf.png)
Substitute 12 for s:
![w=4(12)-13](https://img.qammunity.org/2021/formulas/mathematics/college/thfl28zdhex7xrhce96tny7as6v4goklxv.png)
Multiply and subtract:
![w=48-13=35](https://img.qammunity.org/2021/formulas/mathematics/college/psb6aympfeieb4npdffzjb9mwmd38pqj3z.png)
So, our length is 19 and our width is 35.
The choice that reflects this is D.
And we're done!