Perimeter Equations: Equal Shapes Math Challenge

A rectangle has a length of 3x + 2 and a width of x + 5. If another rectangle has a length of 4x and a width of 2x - 1, set up an equation to find x when both rectangles have equal perimeter.

• 2

• 3

• 5

• 4

Tags

CCSS.8.EE.C.7B

The perimeter of a square is equal to the perimeter of a rectangle. If the side of the square is 2x + 3 and the rectangle has a length of x + 7 and a width of 3, write an equation to find x.

• 2x + 10

• 4/3

• 5

• x + 4

Tags

CCSS.8.EE.C.7B

Two triangular gardens have equal perimeters. The first garden has sides of lengths 2x, 3x - 1, and x + 4. The second garden has sides of lengths 5x - 2, x + 1, and 3x. Set up an equation to find x.

• 4/3

• 3

• 5/2

• 2

Tags

CCSS.3.MD.D.8

A park is designed in the shape of a rectangle. The length is 5 meters more than twice the width. If another rectangular area has a width of x and a length of 3x - 1, find x when both areas have equal perimeters.

• 5

• 4

• 3

• 2

Tags

CCSS.8.EE.C.7B

A rectangular swimming pool has a length of 4x + 6 and a width of 2x + 2. A nearby rectangular hot tub has a length of 3x + 4 and a width of x + 8. Set up an equation to find x when both have equal perimeters.

• 1

• 2

• 5

• 3

Tags

CCSS.8.EE.C.7B

The perimeter of a rectangular field is equal to the perimeter of a square field. If the square has a side length of 3x + 1 and the rectangle has a length of 2x + 5 and a width of x + 3, find x.

• 4

• 2

• 3

• 1

Tags

CCSS.8.EE.C.7B

Two playgrounds are designed with equal perimeters. The first playground is a rectangle with a length of 6x and a width of 2x + 4. The second playground is a square with a side length of 4x. Set up an equation to find x.

• x = 4

• No valid solution for x.

• x = 2

• x = 3

Tags

CCSS.8.EE.C.7B

A rectangular garden has a length of 5x - 3 and a width of 2x + 1. If another rectangular garden has a length of 3x + 5 and a width of 4, find x when both gardens have equal perimeters.

• 2.75

• 4.25

• 3.0

• 1.5

Tags

CCSS.HSA.REI.A.2

A rectangular classroom has a length of 2x + 10 and a width of x + 5. A storage room has a length of 3x and a width of 2x - 2. Set up an equation to find x when both rooms have equal perimeters.

• 8

• 6

• 10

• 12

Tags

CCSS.8.EE.C.7B

Two rectangular plots of land have equal perimeters. The first plot has dimensions of 3x + 2 and 2x + 4, while the second plot has dimensions of 4x and x + 6. Write an equation to find x.

• x can be any real number.

• x is equal to 5.

• x cannot be greater than 10.

• x must be a positive integer.

Tags

CCSS.8.EE.C.7B