A rectangle has a perimeter of 20 cm. If the measures of sides area whole number of centimeters, Find the five possible pairs of value for the length and width. with full process
Answers
In a rectangle we know that two opposite sides are equal. So, PQ = SR and PS = QR
If PS = l and PQ = b
Perimeter of a Rectangle
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Perimeter of the rectangle = PQ + QR + RS + SP
= b +l + b + l
= 2b +2l
Again,
ABCD is a rectangle. We know that the opposite sides of a rectangle are equal.
Perimeter of a Rectangle
AB = CD = 5 cm and BC = AD = 3 cm
So, the perimeter of the rectangle ABCD = AB + BC + CD + AD = 5 cm + 3 cm + 5 cm + 3 cm = 16 cm
It can be written as 5 cm + 5 cm + 3 cm + 3 cm
= (2 × 5) cm + (2 × 3) cm
= 2 (5 + 3) cm
= 2 × 8 cm
= 16 cm
We add length and breadth twice to find the perimeter of a rectangle.
Perimeter of a rectangle = 2 (length + breadth)
Let us consider some of the examples on perimeter of a rectangle:
1. The length of a rectangle is 4 cm and its breadth is 2 cm. Find its perimeter.
Solution:
Length = 4 cm
Breadth = 2 cm
Examples on Perimeter of a Rectangle
Therefore, perimeter of the rectangle
= 2 (length + breadth)
= 2 (4 + 2) cm
= 2 × 6 cm
= 12 cm
2. Find the perimeter of the rectangle ABCD whose sides are 6 cm and 5 cm.
Solution:
Perimeter of Rectangle
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The perimeter of the rectangle ABCD
= 6 cm + 5 cm + 6 cm + 5cm
= 22 cm
3. A rectangular swimming pool is 9 m long and 4 m broad. Find the area of the swimming pool.
Solution:
Length of the rectangular swimming pool = 9 m
Breadth of the rectangular swimming pool = 4 m
Therefore, perimeter of the rectangle swimming pool
= 2 (length + breadth)
= 2 (9 + 4) m
= 2 (13) m
= 2 × 13 m
= 26 m
4. The length of a rectangle is 4.5 m and the breadth is 1.5 m. Find the perimeter.
Solution:
Length = 4.5 m
Breadth = 1.5 m
Perimeter of a Rectangle Problems
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Perimeter = 2 (length + breadth)
= 2 × (4.5 m + 1.5 m)
= 2 × 6 m
= 12 m
Therefore, the perimeter is 12 m.
5. A rectangle display board is measuring 8 m by 6 m. Robert wants to add a ribbon border around the display board. What is the length of ribbon that he will need? If the cost of the ribbon is $ 15 per metre then how much money does Robert needs to buy the ribbon?
Solution:
Length of the display board = 8 m
Breadth of the display board = 6 m
Perimeter of the display board = 2(Length + Breadth)
= 2(8 + 6) m
= 2 × 14 m
= 28 m.
Cost of ribbon is $15 per metre.
Therefore, total cost for 28 m long ribbon = $15 × 28
= $420.
Questions and Answers on Perimeter of a Rectangle:
1. Sam is running around a rectangular park of length 450 m and breadth 300 m. Find the total distance covered by him if he takes 10 rounds of the park.
Answer:
15000 m
2. A gardener wants to fence its rectangular garden with a wire. The length and breadth of the garden is 25 m and 16 m respectively. Find the length of the wire he must buy.
Answer:
82 m
Answer:
Perimeter of Rectangle = 2(L+B) = 20cm
2(L+B) = 20cm
(Transversing 2 to RHS)
L+B = 20cm / 2
L+B = 10cm
So, we need the values of L and B to add up to 10cm
Luckily, we have such values
Length (L) Breadth (B)
0cm 10cm
1cm 9cm
2cm 8cm
3cm 7cm
4cm 6cm
5cm 5cm
6cm 4cm
7cm 3cm
8cm 2cm
9cm 1cm
10cm 0cm
Here, we can eliminate 0cm, 10cm as possible L and B values, as such rectangles cannot exist
We can even eliminate the values where L is smaller than B
The remaining values are
Length (L) - 5cm, 6cm, 7cm, 8cm, 9cm
Breadth (B) - 5cm, 4cm, 3cm, 2cm, 1cm
You might be wondering, if both the L and B are same, doesn't it become a Square?
Yes, you are correct. It is a Square. But, a Square is a special Rectangle in which all the sides are equal
You can check it for yourself