Question

The length of the rectangular backyard is 5 meters longer than the width. The perimeter is 110 meters. Find the width and length.

a) Width = 12, Length = 17

b) Width = 15, Length = 20

c) Width = 18, Length = 23

d) Width = 20, Length = 25

Answer 1

To find the width and length of the rectangular backyard, we set up equations based on the perimeter and the relationship between length and width, which yields a width of 25 meters and a length of 30 meters.

Step-by-step explanation:

The question involves finding the width and length of a rectangular backyard with a given perimeter and a relationship between the length and width. To solve this, we can set up two equations based on the information given.

Let W be the width and L be the length of the backyard. The problem states that the length is 5 meters longer than the width, so we can write that as L = W + 5. The perimeter (P) of a rectangle is calculated by P = 2L + 2W. We know the perimeter is 110 meters, so we substitute our expression for L into this formula:

110 = 2(W + 5) + 2W.

To find the width and length:

1. Simplify the equation: 110 = 2W + 10 + 2W = 4W + 10.
2. Subtract 10 from both sides: 100 = 4W.
3. Divide both sides by 4: W = 25.
4. Plug the width back into the expression for length: L = 25 + 5 = 30.

The width is 25 meters and the length is 30 meters, which corresponds to option d) Width = 20, Length = 25 if we are considering the choices given in meters rather than feet.