Perimeter of a rectangle is 42cm and its area 20cmsq
.Find sum of length and breadth
.Form a second degre equation connecting length breadth and area
Find length and breadth of rectangle
Answers
Answer:
Step-by-step explanation:
length =l
breadth = b
l x b = 20 AREA
2l + 2b = 42 PERIMETER
2l = 42 - 2b
l = 21 -b
Substitute the value for l into the equation for AREA
21-b x b = 20
21b -b^2 = 20
21-b =20
b = 1
l = 20
SUM length and breadth = 21 cm
Length = 20 cm
Breadth = 1 cm
l x b = AREA = 20 cm2
Given:
✰ Perimeter of a rectangle = 42 cm
✰ Area of a rectangle = 20 cm²
To find:
✠ The sum of length and breadth.
✠ Form a second equation connecting length, breadth and area.
- Find length and breadth of rectangle
Solution:
✭ Perimeter of rectangle = 2 ( l + b ) ✭
Where,
- l is the length of a rectangle.
- b is the breadth of a rectangle.
➛ 2 ( l + b ) = 42
➛ 2l + 2b = 42
➛ 2l = 42 - 2b
➛ l = (42 - 2b)/2
➛ l = 21 - b ...①
Let's find out the sum of length and breadth first.
➛ 2 ( l + b ) = 42
➛ l + b = 42/2
➛ l + b = 21 cm
∴ The sum of length and breadth = 21 cm
Now,
✭ Area of rectangle = l × b ✭
Where,
- l is the length of a rectangle.
- b is the breadth of a rectangle.
➛ l × b = 20 ...eq②
Substituting the value of eq① in eq②, we have:
➛ (21 - b) × b = 20
➛ 21b - b² = 20
➛ - b² + 21b - 20 = 0
➛ - b² + 20b + 1b - 20 = 0
➛ -b (b - 20) +1 ( b - 20) = 0
➛ (b - 20) ( - b + 1 ) = 0
Taking, because breadth can't be negative, therefore take positive.
⟹ b - 20 = 0
⟹ b = 20
∴ The breadth of a rectangle = 20 cm
Now, let's find out length by using eq② and substituting the value of breadth in eq② i.e, area of rectangle.
⟹ l × b = 20
⟹ l × 20 = 20
⟹ l = 20/20
⟹ l = 1
∴ The length of a rectangle = 1 cm
➛ Sum of length and breadth
➛ 1 + 20
➛ 21 cm
∴ The sum of length and breadth = 21 cm
Hence Proved!!
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