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

Question

1830 views around the world

You can reuse this answer
Creative Commons License

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#