# What is the area and perimeter of a rectangle whose width is (x+y) and length is (3x+2y)?

Sep 6, 2015

Area: $3 {x}^{2} + 5 x y + 2 {y}^{2}$
Perimeter: $8 x + 6 y$

#### Explanation:

For a rectangle of length $l$ and width $w$, the formulas for area and perimeter look like this

$\textcolor{b l u e}{\text{area} = A = w \cdot l}$

$\textcolor{b l u e}{\text{perimeter} = P = 2 \cdot \left(l + w\right)}$

For your rectangle, you know that

$w = x + y \text{ }$ and $\text{ } l = 3 x + 2 y$

This means that the area of the rectangle will be

$A = w \cdot l$

$A = \left(x + y\right) \cdot \left(3 x + 2 y\right) = 3 {x}^{2} + 5 x y + 2 {y}^{2}$

The rectangle's perimeter will be

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

$P = 2 \cdot \left(x + y + 3 x + 2 y\right)$

$P = 2 \cdot \left(4 x + 3 y\right) = 8 x + 6 y$