Question

The length of a rectangle is three times its width. If the perameter of rectangle is 100 meter , find lenth and width of the rectangle

Answer 1

Given :-

The length of a rectangle is three times its width.

Perimeter of the rectangle = 100 m

To Find :-

The length of the rectangle.

The width of the rectangle.

Analysis :-

Consider the width as a variable. Then the length would be thrice of it.

Make an equation accordingly and find the width.

Substitute the value in the length as well.

Solution :-

We know that,

• l = Length
• b = Breadth
• p = Perimeter

Let the length and breadth be 3x and x respectively.

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ rectangle=2(Length + Breadth)}}$

Given that,

Perimeter of the rectangle = 100 m

Substituting their values,

100 = 2(3x + x)

100 = 2(4x)

100 = 8x

Finding x,

x = 100/8

x = 12.5

Therefore,

Breadth (b) = 12.5m

Length = 3x

= 3 × 12.5

= 37.5 m

Hence, the length and breadth are 37.5 m and 12.5 m respectively.

Answer 2

Answer:

★ ANSWER :

Width of rectangle = 12.5m

Length of rectangle = 37.5m

Step-by-step explanation:

★ QUESTION :

The length of a rectangle is three times its width. If the perimeter of rectangle is 100m , find lenth and width of the rectangle.

★ GIVEN :

• Perimeter of rectangle = 100m
• Length of rectangle = 3 × Width of rectangle

★ HOW TO SOLVE ?

Consider the width of the rectangle as a variable. Then the length of rectangle will be thrice of it.

Form an equation with the length and width of rectangle as perimeter and equate to the given perimeter of the rectangle.

Find the values of length and width.

★ CONCEPT USED :

• Perimeter of rectangle = 2(Length + Breadth)
• P of rectangle = 2(l + b)
• P = Perimeter
• l = Length
• b = Breadth

★ SOLUTION :

Let the width of the rectangle be x.

Therefore , the length of the rectangle = 3 × Width of rectangle

Length of rectangle = 3 × x

Length of the rectangle = 3x

Perimeter of rectangle = 2(l + b)

Perimeter of rectangle = 2(x + 3x)

Perimeter of rectangle = 2 × 4x

Perimeter of rectangle = 8x. ------- (1)

According to Question ,

Perimeter of rectangle = 100m. ------- (2)

Equating Equation (1) and (2). We get,

8x = 100m

→ x = 100m/8

→ x = 12.5m

Width of rectangle = x

Width of rectangle = 12.5m

Length of rectangle = 3 × Width of rectangle

Length of rectangle = 3 × x

Length of rectangle = 3 × 12.5m

Length of rectangle = 37.5m

★ ANSWER :

Width of rectangle = 12.5m

Length of rectangle = 37.5m

HOPE IT HELPS YOU !

THANKS !