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?

Jul 26, 2015

Width: 65 m
Length: 90 m

Explanation:

The perimeter of a reactangle is given by the formula

$P = 2 \cdot \left(w + L\right)$, 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

$P = 2 \cdot \left[w + {\underbrace{\left(w + 25\right)}}_{\textcolor{b l u e}{\text{=L}}}\right]$

$P = 2 \cdot \left(w + w + 25\right) = 2 \cdot \left(2 w + 25\right) = 4 w + 50$

This means that the width of the rectangle will be

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

$w = \frac{260}{4} = \textcolor{g r e e n}{\text{65 m}}$

The length of the rectangle will be

$L = w + 25 = 65 + 25 = \textcolor{g r e e n}{\text{90 m}}$

Check to see if the values you got are correct

$P = 2 \cdot \left(65 + 90\right) = 2 \cdot 155 = 310 \to$the two values are valid!