Question

The length of a rectangle is 5 more than twice the width. if the perimeter of the rectangle is 76 meters, find the dimensions of the rectangle and choose the equation that represents the perimeter:
1. 76=2w+5
2. 76=2w+2(2w+5)
3. 76=w+2w+5
4. 76=2w+(2w+5)

Answer 1

Answer:

Dimensions: 11 meters by 27 meters

2. $76=2w+2(2w+5)$

Step-by-step explanation:

Finding Dimensions:

The perimeter of a rectangle can be written as $2l+2w$ where $l$ is the length and $w$ is the width. It is given that the length is 5 more than twice the length of width and the perimeter of the rectangle is 76 meters.

With this information we can write:

Length = $2w+5$

$2(2w+5)+2w = 76$ (perimeter of the rectangle)

$4w+10+2w=76$

$6w=66$

$w=11$

Length = $2(11)+5$

Length = $27$

∴ The dimensions of the rectangle is 11 meters by 27 meters.

Perimeter

Since the length can be written as $2w+5$, the equation that represents the perimeter of the rectangle is $76=2w+2(2w+5)$