Question

The length of a rectangle is six feet more than three times the wide the perimeter is 36 feet. Find the length and width.

Answer 1

Width is 3 feet

Length is 15 feet

Explanation:

Formula for perimeter of a rectangle;

Perimeter = 2(length + width)

- let the width be w

- Length = (3w + 6) feet

Therefore;

`{ \rm{perimeter = 2 \{(3w + 6) + w \}}} \\ { \rm{perimeter = 2 \{(3w + w) + 6 \}}} \\ { \rm{perimeter = 2(4w + 6)}} \: \: \: \: \: \: \: \: \: \: \: \: \:`

But perimeter is 36 feet

`{ \rm{36 = 2(4w + 6)}} \\ \\ { \rm{ (36)/(2) = (2(4w + 6))/(2) }} \\ \\ { \rm{18 = 4w + 6}} \: \: \: \: \: \: \: \: \: \\ { \rm{4w + 6 = 18}} \: \: \: \: \: \: \: \: \\ { \rm{4w = 18 - 6}} \: \: \: \: \: \: \: \: \\ { \rm{4w = 12}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \rm{w = 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:`

Therefore;

width is 3 feet

Length = 3w + 6 = (3×3) + 6 = 15 feet