Answer:
![a) \quad l = (P-2w)/(2)](https://img.qammunity.org/2023/formulas/mathematics/high-school/oeo11rzjfafqqyq5b7g8j70c8wah48t6k5.png)
![b) \quad 26 \ inches](https://img.qammunity.org/2023/formulas/mathematics/high-school/73r97048y07m5mp52mps548zh17hnffi0l.png)
Step-by-step explanation:
Perimeter = 2(Length + Width)
In short form:
P = 2l + 2w
Here make "l" the subject:
![\rightarrow P = 2l + 2w](https://img.qammunity.org/2023/formulas/mathematics/high-school/mg7r309i39n3vqpj9cgen3efkx6xjz840i.png)
relocate term w
![\rightarrow P-2w = 2l](https://img.qammunity.org/2023/formulas/mathematics/high-school/kp91bl57hf9232ry2xc446qnib1qgos1r9.png)
dividing both sides by 2
![\rightarrow (P-2w)/(2) = l](https://img.qammunity.org/2023/formulas/mathematics/high-school/sbvq3w0p2wwug0itfddr6x0cntn8v4728c.png)
Now find the length of picture frame:
Given: P = 84 inches, W = 16 inches
![\rightarrow l = (84-2(16))/(2)](https://img.qammunity.org/2023/formulas/mathematics/high-school/8flxzs835f1ieo7gl5a2cm35haplz59ncd.png)
evaluate
![\rightarrow l =26](https://img.qammunity.org/2023/formulas/mathematics/high-school/hw3lh3tykh7j9br9ne6smbu5yuc3u2tdhf.png)
Hence, the length of the picture frame is 26 inches.