Question

The length of a rectangle is 6 feet less than 4 times the width. If the perimeter is 68 feet, find the length and the width of the rectangle.

Answer 1

Length = 26 feet; Width = 8 feet

Explanation:

Let:

x = Length of rectangle

y = Width of rectangle

4 times the width = 4y

∴ 6 less than 4 times the width = 4y - 6

Perimeter of a rectangle = 2 × [Length + Width]
68 = 2 × [(4y - 6) + y]

Expand the brackets or parenthesis by applying the Distributive Law and bring the like terms together:

68 = 2 × [4y - 6 + y]
68 = 2 × [5y - 6]

68 = 10y - 12

68 + 12 = 10y

Isolate y by making it the subject of the equation:

80 = 10y

y =
`(80)/(10)`

y = Width of rectangle: 8 feet

Substitute y into the equation to calculate x:

x = 4(8) - 6

x = Length of rectangle =
`(32 - 6)` feet

x = 26 feet