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

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Answer 1 · 2015-09-06T11:56:40

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

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

$color(blue)("area" = A = w * l)$

$color(blue)("perimeter" = P = 2 *(l + w))$

For your rectangle, you know that

$w = x + y" "$ and $" "l = 3x + 2y$

This means that the area of the rectangle will be

$A = w * l$

$A = (x+y) * (3x + 2y) = 3x^2 + 5xy + 2y^2$

The rectangle's perimeter will be

$P = 2 *(l + w)$

$P = 2 * (x + y + 3x + 2y)$

$P = 2 * (4x + 3y) = 8x + 6y$