Perimeter of Rectangle

1. Suppose that the perimeter of a rectangle is 48 cm and the length is three times the width. What are the dimensions of this rectangle?

Solution:
Let the length of rectangle be "L" and the width be "W"
Perimeter = Sum of all sides
P = L + L + W + W
P = 2L + 2W
Length = 3 x Width -----> L = 3W
P = 2( 3W ) + 2W
P = 6w + 2W
P = 8W
P = 48 ( which is given )
So 8W = 48, dividing by 8 on both sides
W = 48 / 8, that is W = 6
So L = 3W , L = 3(6) = 18
Answer: Length = 18 cm , Width = 6cm

2. A rectangular swimming pool measures 25ft by 50ft and has a 6 foot wide sidewalk around it. How much fencing is needed to enclose the sidewalk?

Solution:
Before we go into the explanation of the problem, let us draw the diagram for the problem.


The amount of fencing needed to enclose the sidewalk surrounding the swimming pool is nothing but the perimeter of the total rectangle (the region including the blue and grey rectangle).
So the length of the total rectangle will be length of the blue rectangle + the 6 foot on the left side + 6 foot on the right side
Length of total rectangle = 50 + 6 + 6 = 62 ft
Similarly the width of the total rectangle will be width of the blue rectangle + 6 foot on top + 6 foot below.
Width of total rectangle = 25 + 6+ 6 = 37 ft

L = 62 ft and W = 37 ft
Perimeter = 2L + 2W
P = 2(62) + 2(37)
P = 124 + 74
P = 198 ft
Answer: 198ft of fencing is needed to enclose the sidewalk that surrounds the swimming pool.

3. A rectangle has a length of 8 and a diagonal of 10. What is the perimeter of this rectangle?

Solution:
Let us draw the rectangle first.



To find the value of 'x' we shall use Pythagoras theorem
x² + 8² = 10²
x² = 10² - 8²
x² = 100 - 64
x² = 36
x = sq root (36)
x = 6

So L = 8cm and W = 6cm
Perimeter = 2L + 2W
P = 2(8) + 2(6)
P = 16 + 12
P = 28 cm

Answer: Perimeter of the rectangle is 28cm

Perimeter

The perimeter of a polygon is the distance around the outside of the polygon. A polygon is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units. Perimeter is the total distance around any polygon (any 2D figure). Perimeter can be calculated by adding the length of the sides. Examples: The perimeter can be used to calculate the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter.

Perimeter of any figure = Sum of all the sides of the figure

We shall see the very basic word problems in perimeter in this section:

1. Find the perimeter of a rectangle whose length is 8cm and width is 3cm.

Solution:
The perimeter of rectangle can be calculated as the sum of all the sides, which is
L + L + W + W = 2L + 2W
Where L = length and W = width
Here L = 8cm and W = 3cm
Perimeter = 2L + 2W
= (2x8) + (2x 3)
= 16 + 6
= 22cm

2. Find the perimeter of triangle whose sides are given by 3cm , 4cm and 5cm.

Solution:
Sum of all the sides gives the perimeter, here the three sides are 3 , 4 and 5
So perimeter = 3 + 4 + 5
= 12cm

3. Find the perimeter of the circle with radius 5cm

Solution:
Perimeter of circle is nothing but the circumference of the circle.
Circumference of the circle = 2 π r
Here r = radius = 5 cm
Circumference = 2π ( 5) = 10 π cm
π = 3.14
So circumference = 10 x 3.14 = 31.4cm

Geometry: Basic Definitions

What is Geometry?

Geometry is a branch of mathematics that is concerned with the properties of configurations of geometric objects - points, (straight) lines, and circles being the most basic of these. The two main areas of geometry are plane geometry and solid geometry. Plane geometry deals with two dimensional (flat or planar) shapes like circles, lines, and triangles. Three dimensional shapes like cubes, spheres, and cones are studied in solid geometry.

The basic terms