Question

The length of a rectangle is 4 more than twice the width. The perimeter of the rectangle is 56 units. What is the width of the rectangle?

Option 1: 8 units
Option 2: 10 units
Option 3: 12 units
Option 4: 14 units

Answer 1

The width of the rectangle is 8 units, calculated by setting up an equation using the given perimeter of 56 units and the relationship between the length and the width of the rectangle.

Step-by-step explanation:

To find the width of the rectangle when the perimeter is 56 units and the length is 4 more than twice the width, let's represent the width as w units and the length as l units. The length can be expressed as l = 2w + 4. The perimeter of a rectangle is found by the formula P = 2l + 2w. Substituting the value of l into the formula and using the given perimeter, we have:

56 = 2(2w + 4) + 2w

56 = 4w + 8 + 2w

56 = 6w + 8

Subtract 8 from both sides:

48 = 6w

Divide both sides by 6 to find the width:

w = 8 units

Therefore, the width of the rectangle is 8 units, which corresponds to Option 1.

Answer 2

option 1 : 8 units

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2( length + width )

let width be w, then length = 2w + 4 ( 4 more than twice the width )

given P = 56 units , then

56 = 2(2w + 4 + w)

56 = 2(3w + 4) ( divide both sides by 2 )

28 = 3w + 4 ( subtract 4 from both sides )

24 = 3w ( divide both sides by 3 )

8 = w

Then the width of the rectangle is 8 units