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