The length of a rectangle exceeds its breadth by 5cm. In the new rectangle the length becomes twice of original rectangle and breadth is increased by 5cm, then the perimeter of the new rectangle increases by 21cm. Find the dimensions of the original rectangle.
Answers
Answer:
Step-by-step explanation:
The length and breadth are 14 cm and 10 cm
Step-by-step explanation:
Given that the length of a rectangle exceeds its breadth by 4 cm .if length and breadth are each is increased by 3 cm , the area of the new rectangle is 81 square cm more than the given rectangle.
we have to find the length and breadth of rectangle.
Let the breadth of rectangle be x cm
∴ The length is x+4
Now, length and breadth are each is increased by 3 cm
New length=(x+4)+3=x+7
New breadth=x+3
As the area of the new rectangle is 81 square cm more than the given rectangle.
⇒
∴
The length and breadth are 14 cm and 10 cm
Let :
- Original Breadth of rectangle = x
- Perimeter of original rectangle = P
Given :
- Original length = Original Breadth + 5cm
- Length of new rectangle = 2× original length
- Breadth of new rectangle = 5cm + original breadth
- Perimeter of new rectangle = 21cm + Perimeter of original rectangle
Formula used :
- Perimeter of rectangle = 2(length + breadth)
Solution :
Perimeter of original rectangle = 2×(original length + original breadth)
P = 2× { (x+5)+(x)}
P = 2(2x+5) ............equation 1
Perimeter of new rectangle = 2× ( length of new rectangle + breadth of new rectangle)
- Perimeter of new rectangle = P + 21
- Length of new rectangle = 2(x+5) = 2x + 10
- Breadth of new rectangle = (x+5)
Perimeter of new rectangle = 2× { (2x+10)+(x+5)}
P + 21 = 2×(3x+15)
putting value of P from equation 1, we get;
=> 2(2x+5) + 21 = 2(3x+15)
=> 4x + 10 + 21 = 6x + 30
=> 6x - 4x = 31 - 30
=> 2x = 1
=> x = (1/2)
Therefore,
Breadth of original rectangle = x = 0.5 cm
Length of original rectangle = (x+5) = 5.5 cm
ANSWER :
- Length of original rectangle = 5.5 cm
- Breadth of original rectangle = 0.5 cm