Question

1. Length of a rectangle is three times its breadth Perimeter of the rectangle is t0 cm. Find its length and
width​

Answer 1

Correct Question ::

Length of a rectangle is three times its breadth Perimeter of the rectangle is 10cm. Find its length and width.

Answer ::

• The length of rectangle = 3.75cm
• The breadth of rectangle = 1.25cm.

Step-by-step explanation ::

To Find:-

• The length & the breadth of the rectangle

Solution:-

Given that,

• Length of the rectangle is three times the breadth.
• Perimeter of rectangle = 10cm

Let us assume the length as 3x and the breadth as x,

As we know that,

Perimeter of rectangle = 2 ( l + b ),

Where,

• l = Length
• b = Breadth

Therefore,

➦ 2 ( Length + Breadth ) = 10

➦ 2 ( 3x + x ) = 10

➦ 3x + x = 10 / 2

➦ 4x = 5

➦ x = 5 / 4

➦ x = 1.25

The value of x is 1.25.

ACCORDING THE QUESTION,

➻ Length of rectangle is,

➦ 3x

➦ 3 × 1.25

➦ 3.75

The length of rectangle is 3.75cm.

➻ Breadth of rectangle is,

➦ x

➦ 1.25

The breadth of rectangle is 1.25cm.

Answer 2

Correct Question :

Length of a rectangle is three times its breadth Perimeter of the rectangle is 10 cm. Find its length and breadth.

GiveN :

Analysis :

First we have to determine the dimensions i.e., length and breadth of the rectangle by the given information. Then putting the values in the equation we can find the actual length and breadth of the rectangle.

Solution :

Let us assume that the breadth is "x" cm and length is "3x" cm.

• Perimeter = 10 cm.

We know that if we are given the length, breadth and perimeter of the rectangle we have the required formula to find the perimeter,

Perimeter of rectangle = 2( length + breadth)

where,

• Length = 3x cm
• Breadth = x cm
• Perimeter = 10 cm

By using the formula of the perimeter of the rectangle and substituting the values,

⇒ Perimeter of rectangle = 2( length + breadth)

⇒ 10 = 2(3x + x)

⇒ 10 = 2(4x)

⇒ 10 = 2 × 4x

⇒ 10 = 8x

⇒ 10/8 = x

⇒ 1.25 = x

∴ x = 1.25.

The dimensions are :

1. Length = 3x = 3 × 1.25 = 3.75 cm
2. Breadth = x = 1.25 cm

The length and breadth are 3.75 cm and 1.25 cm respectively.

VerificatioN :

Perimeter of rectangle = 2( length + breadth)

where,

• Length = 3.75 cm
• Breadth = 1.75 cm
• Perimeter = 10 cm

By using the formula of the perimeter of the rectangle and substituting the values,

⇒ Perimeter of rectangle = 2( length + breadth)

⇒ 10 = 2(3.75 + 1.75)

⇒ 10 = 2(5)

⇒ 10 = 2 × 5

⇒ 10 = 10

∴ LHS = RHS.

• Hence verified.