the perimeter of a rectangle is 80 cm and the area is 375 sq then the length and breadth of the rectangle is
Answers
Step-by-step explanation:
perimeter = 80 cm
area = 375 sqcm
perimeter = 2 (l+b) = 80
l+b = 80/2 = 40
l+b = 40
Area = lb = 375
(l+b)^2 = l^2 + b^2 + 2lb
1600 = l^2 +b^2 + 2×375
1600 = l^2 + b^2 + 750
l^2 + b^2 = 1600-750 = 850
l^2 + b^2 = 850
(l-b)^2 = l^2 + b^2 - 2lb
(l-b)^2 = 850 - 2×375
(l-b)^2 = 850- 750
(l-b)^2 = 100
l+b = 40
====eq2
eq1+ eq2 = l-b+l+b =40+10 = 50
2l =50
l = 50/2
l=25
l-b = 10
l-10=b
b=25-10
b=15
LENGTH = 25 cm
BREADTH = 15 cm
Required Answer :
When length of the rectangle = 25 cm, breadth = 15 cm
When length of the rectangle = 15 cm, breadth = 25 cm
Given :
- Perimeter of rectangle = 80 cm
- Area of rectangle = 375 cm²
To find :
- Length and breadth of the rectangle
Solution :
Let the breadth of rectangle be x cm
Using formula,
- Perimeter of rectangle = 2(l + b)
where,
- l denotes the length of the rectangle
- b denotes the breadth of the rectangle
Substituting the given values :
⇒ 80 = 2(l + x)
⇒ 80/2 = l + x
⇒ 40 = l + x
⇒ 40 - x = l
Hence,
⇒ Length of the rectangle = (40 - x) cm
⇒ Breadth of the rectangle = x cm
Using formula,
- Area of rectangle = l × b
Substituting the given values :
⇒ 375 = (40 - x)(x)
⇒ 375 = 40x - x²
⇒ x² - 40x + 375 = 0
⇒ A quadratic equation is formed whose product is 375x²
⇒ x² - 25x - 15x + 375 = 0
⇒ x(x - 25) - 15(x - 25) = 0
⇒ (x - 15)(x - 25) = 0
⇒ (x - 15) = 0 or (x - 25) = 0
⇒ x = 15 or x = 25
Substituting the value of x :
When x = 15 :
Length :
⇒ Length = (40 - x)
⇒ Length = (40 - 15)
⇒ Length = 25 cm
Breadth :
⇒ Breadth = x
⇒ Breadth = 15 cm
When x = 25 :
Length :
⇒ Length = (40 - x)
⇒ Length = (40 - 25)
⇒ Length = 15 cm
Breadth :
⇒ Breath = x
⇒ Breadth = 25 cm
Therefore,
- When length of the rectangle = 25 cm then the breadth of the rectangle = 15 cm
- When length of the rectangle = 15 cm then the breadth of the rectangle = 25 cm