what is this um
The length of a rectangle is 3 more than 4 times its width. The perimeter of the rectangle is 86 inches. What is the length of the rectangle?

23 in.
27 in.
31 in.
35 in.

Question

what is this um 
The length of a rectangle is 3 more than 4 times its width. The perimeter of the rectangle is 86 inches. What is the length of the rectangle?

       23 in.
       27 in.
       31 in.
       35 in.

anonymous · Answer

|dw:1381252867826:dw|
Sorry if it's abit long, it's pretty simple though
$$
b = 4 \cdot a + 3 \
\text{perimeter} = 2\cdot b + 2 \cdot a \
\text {perimeter} = 2 \cdot (4a + 3) + 2a \
\text {perimeter} = 8a + 6 + 2a \
\text {perimeter} = 10a + 6 \
\text {perimeter} = 86_{inches}\
10a + 6 = 86 \
10 a = 80 \
a = 8_{inches} \
b = 4\cdot a + 3 = 4\cdot8 + 3 = 32 + 3 = 35_{inches}
$$