The perimeter of the field is 320 m. If the length of a rectangular field is thrice its breadth, then find the area.
Answers
Answer:
length = 120 m
breadth = 40 m
Step-by-step explanation:
Perimeter of rectangle = 2 (l+b)
let breadth be x and length be 3x
320 = 2(3x + x )
320 = 2 (4x)
320 = 8x
320 / 8 = x
x = 40 = breadth
3x = 40× 3 = 120
1. Question
The sum of present ages of John and his father is 58 years. If john is 24 years younger than his father, then find the present of John's father.
• Given
- The sum of present ages of John and his father = 58 years
- John is 24 years younger than his father.
• To find
- Present age of John's father
• Concept
We are given with the ages of John and his father.
• This can be solved in two ways -
- When we will let the age of John = x years
- Then father's age = x + 24 years
- When, John's age = x - 24 years
- Then father's age = x years
Then, add both the ages and keep it equal to 58. From there we will get the value of x. By substituting the value of x in John and his father's age we will get our answer.
• Solution
1st method -
Let the age of John be x and his father's age be x + 24 years.
According to the question,
⟶ x + x + 24 = 58
⟶ 2x + 24 = 58
⟶ 2x = 58 - 24
⟶ 2x = 34
⟶ x = 34/2
⟶ x = 17
The value of x = 17
- John's age = x = 17 years
- His father's age = x + 24 = 17 + 24 = 41 years
Method 2
Let the age of John be x - 24 years and his father's age be x years.
According to the question,
⟶ x - 24 + x = 58
⟶ 2x = 58 + 24
⟶ 2x = 82
⟶ x = 82/2
⟶ x = 41
The value of x = 41.
- John's age = x - 24 = 41 - 24 = 17 years
- His father's age = 41 years.
________________________________
Let's verify -
The sum of present ages of John and his father = 58 years
⟶ 17 + 41
⟶ 58 years.
Hence, verified.
2. Question
The perimeter of the field is 320 m. If the length of a rectangular field is thrice its breadth, then find the area.
• Given
- Perimeter of the field = 320 m
- Length of the rectangular field is thrice its breadth.
• To find
- Area of the field
• Solution
Let the breadth be x and the length be 3x.
Using formula,
Perimeter = 2(l + b)
where,
- l = length
- b = breadth
Substituting the values,
⟶ 320 = 2(3x + x)
⟶ 320 = 2(4x)
⟶ 320 = 8x
⟶ 320/8 = x
⟶ 40 = x
The value of x = 40
- Length of the field = 3x = 3 × 40 = 120 m
- Breadth of the field = x = 40 m
Using formula,
Area = l × b
where,
- l = length
- b = breadth
Substituting the values,
⟶ 120 × 40
⟶ 4800 m²
Area of the field = 4800 m²