Question

The perimeter of the field is 320 m. If the length of a rectangular field is thrice its breadth, then find the area.

Answer 1

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

Answer 2

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