Question

If a rectangle's length is y−2 and the width is 3y+2 write an expression for the perimeter and an expression for the area.

Answer 1

Area =
`3y^2 - 4y - 4` units square.

Perimeter = 8y units.

Explanation:

Area of a rectangle = length * width.

Perimeter of a rectangle = 2*(length + width).

It is given that length = y−2 units and width = 3y+2 units. To find the area and the area of the rectangle in terms of y, simply put the length and the width in the above area and perimeter equations.

Area = length * width = (y-2)*(3y+2).

Expanding the expression gives:

Area = 3y^2 + 2y - 6y - 4 = (3y^2 -4y - 4) units square.

Similarly,

Perimeter = 2*(length + width) = 2*(y-2 + 3y+2) = 2*4y = 8y units.

Therefore, the expression for the area and the perimeter of the given rectangle is (
`3y^2 - 4y - 4`) units square and (8y) units respectively!!!