Question

The perimeter of a rectangle is 310 m. The length is 25 m greater than the width. What are the length and the width of this rectangle?

Answer 1

Width: 65 m
Length: 90 m

Explanation:

The perimeter of a reactangle is given by the formula

`P = 2 * (w + L)`, where

`w` - the width of the rectangle;
`L` - the length of the rectangle.

You know that the length of the rectangle is 25 m greater than it width. In other words, if you add 25 meters to the rectangle's width, you get its length.

This can be written as

`L = w + 25`

The perimeter will be equal to

`P = 2 * [w + underbrace((w + 25))_(color(blue)("=L"))]`

`P = 2 * (w + w + 25) = 2 * (2w + 25) = 4w + 50`

This means that the width of the rectangle will be

`4w = P - 50 = 310 -50 = 260`

`w = 260/4 = color(green)("65 m")`

The length of the rectangle will be

`L = w + 25 = 65 + 25 = color(green)("90 m")`

Check to see if the values you got are correct

`P = 2 * (65 + 90) = 2 * 155 = 310 ->`the two values are valid!