Question

core: 2)
2. The sides of a rectangle are in the ratio 2:3
a) If the breadth is 2a, what is the length?
b) If the perimeter of the rectangle is 40cm, find the length and breadth?​

Answer 1

Answer:

a) Let the sides of the rectangle be 2x and 3x

then,

A.T.Q-

breadth=2x=2a

x=a

then,3x=3a

b)given-

perimeter of the rectangle=40cm

now,

according to above solution ,sides of rectangle=

3a and 2a

then,

3a+2a=40

5a=40

a=8

sides-

length=3a=24cm

breadth=2a=16cm

Answer 2

Given:

The ratio of the sides of the rectangle = 2:3

The perimeter of the rectangle = 40 cm

To Find:

The length and breadth of the rectangle.

Solution:

The assumption, the breadth of the rectangle = 2a

The perimeter of the rectangle = 2×( length + breadth)

⇒ The perimeter of the rectangle = 40 cm

⇒ 2 × (length + breadth) = 40 cm

⇒ (Length + Breadth) = 20 cm

And the ratio of breadth to the length = 2:3

⇒ length/ breadth = 2/3

⇒ Length = (3/2) × 2a = 3a

Replacing values of the length and the breadth

⇒ perimeter = [2{2a + (3a)}] = 10a = 40 cm

⇒ a = 4 cm

The length of the rectangle = 3a = 12 cm

The breadth of the rectangle = 2a = 8 cm

Hence, the length and breadth of the rectangle are 12cm and 8cm, respectively.