PERIMETER OF SHAPES INVOLVING POLYNOMIALS

Find the perimeter P of the following given all sides are measured in cm:

Problem 1:

Solution :

Perimeter of the shape = 2(x + 2) + 2x + 1 + x

= 2x + 4 + 2x + 1 + x

= 5x + 5

So, the required perimeter is 5x + 5 cm.

Problem 2 :

Solution :

The given figure is a triangle.

Perimeter of the triangle = a + b + c

= 2x - 1 + 2x - 1 + 2x - 1

= 6x - 3

So, perimeter of the triangle is 6x - 3 cm.

Problem 3 :

Solution : 

The given figure is a square.

Perimeter of the square = 4a

= 4(x + 4)

= 4x + 16

So, perimeter of the square is 4x + 16 cm.

Problem 4 :

Solution :

The given figure is a rectangle.

Perimeter of the rectangle = 2(length + width)

Length = x + 3 and width = 2x

= 2(x + 3 + 2x)

= 2x + 6 + 4x

= 6x + 6

So, perimeter of the rectangle is 6x + 6 cm.

Problem 5 :

Solution :

Perimeter of the shape = 2(2x - 1) + 3(x + 2)

= 4x - 2 + 3x + 6

= 7x + 4

So, the required perimeter is 7x + 4 cm.

Problem 6 :

Solution :

Perimeter of the shape = 2(x + 3) + 6(x + 1)

= 2x + 6 + 6x + 6

= 8x + 12

So, the required perimeter is 8x + 12 cm.

Problem 7:

Solution :

The given figure is a triangle.

Perimeter of the triangle = a + b + c

So, perimeter of the triangle is a + b + c cm.

Problem 8 :

Solution :

Perimeter of the shape = 2(2a) + 2(a) + 3a

= 4a + 2a + 3a

= 9a

So, the required perimeter is 9a cm.

Problem 9 :

Solution :

Perimeter of the shape = 2(a + 2) + a

= 2a + 4 + a

= 3a + 4

So, the required perimeter is 3a + 4 cm.