Exploring Perimeters: Algebraic Relationships in Shapes

A rectangular garden has a length of x meters and a width of y meters. If another rectangular garden has a length of 2x meters and a width of 3y meters, what is the relationship between their perimeters?

• The perimeters of both gardens are equal.

• The perimeter of the first garden is greater than the perimeter of the second garden.

• The perimeter of the second garden is half of the perimeter of the first garden.

• The perimeter of the second garden is greater than the perimeter of the first garden.

The perimeter of a square is equal to the perimeter of a rectangle. If the side length of the square is s meters and the rectangle has a length of 2s meters and a width of s meters, express the perimeters algebraically and find the value of s.

• s = 0

• s = 1

• s = 2s

• s = -1

Two playgrounds have the same perimeter. The first playground is a rectangle with a length of 4x meters and a width of 3x meters. The second playground is a square. What is the side length of the square in terms of x?

• 3x

• 4x

• 3.5x

• 2.5x

A rectangular pool has a length of 5 meters and a width of x meters. Another pool has a length of 3 meters and a width of y meters. If both pools have the same perimeter, write an equation to find the relationship between x and y.

• x = y - 2

• x = y + 2

• x = 2y

• x = y - 1

A farmer has two fields. The first field is a rectangle with a length of 6 meters and a width of x meters. The second field is a square. If both fields have the same perimeter, express the side length of the square in terms of x.

• 5 + 0.5x

• 3 + 0.5x

• 2 + 0.5x

• 4 + 0.5x

The perimeter of a rectangular room is 50 meters. If the length is 2x meters and the width is x meters, find the value of x and the dimensions of the room.

• x = 10 meters; Length = 20 meters, Width = 10 meters.

• x = 25/3 meters; Length = 50/3 meters, Width = 25/3 meters.

• x = 15 meters; Length = 30 meters, Width = 15 meters.

• x = 20 meters; Length = 40 meters, Width = 20 meters.

A rectangular box has a length of 3x cm and a width of 4 cm. Another box has a length of 2x cm and a width of 6 cm. If both boxes have the same perimeter, find the value of x.

• 4

• 3

• 5

• 2

Two different shapes have equal perimeters. The first shape is a rectangle with a length of 8 meters and a width of y meters. The second shape is a square. Write an equation to find y in terms of the side length of the square.

• y = 4(side length) - 8

• y = side length - 8

• y = 2(side length) - 8

• y = 8 - side length

A rectangular plot of land has a length of 10 meters and a width of x meters. If a second plot has a length of 5 meters and a width of y meters, and both plots have the same perimeter, express y in terms of x.

• y = x + 10

• y = 2x

• y = x + 5

• y = x - 5

A rectangular classroom has a length of 12 meters and a width of x meters. If another classroom has a length of 8 meters and a width of y meters, and both classrooms have the same perimeter, find the relationship between x and y.

• x = y - 4

• x = y

• x = y - 2

• x = y + 4