Question

4) एका आयताची लांबी ही रुंदीच्या दुपटीपेक्षा 2 सेमी ने जास्त आहे. त्या आयताची परिमिती 82 सेमी असेल, तर त्याची लांबी व रुंदी काढा. / The length of rectangle is 2 cm more than twice its breadth. Perimeter of the rectangle is 82 cm. Find its length and breadth. *

Answer 1

Answer:

Length = 28 cm and breadth = 13 cm

Answer 2

The length and breadth of the rectangle are 21.5 cm and 19.5 cm respectively.

Given:

The length of a rectangle is 2 cm more than twice its breadth.

The perimeter of the rectangle is 82 cm.

To Find:

The length and breadth of the rectangle.

Solution:

Let us assume the:

The length of the rectangle = p cm.

The breadth of the rectangle = b cm.

So, the perimeter of the rectangle = 2x(length + breadth) = 2(p + b).

But we are given that the perimeter of the rectangle is 82 cm.

⇒ 2(p + b) = 82

⇒ p + b = 41     ........................(I)

It is also given to us that the length of the rectangle is 2 cm more than twice its breadth.

⇒ p = b + 2

⇒ p - b = 2     ........................(II)

Adding (I) and (II) we get

(p + q) + (p - q) = 41 + 2

⇒ 2p = 43

⇒  p = 21.5

Hence, the length of the rectangle, p = 21.5 cm.

Putting the value of 'p' in (I), we get

21.5 + b = 41

⇒ b = 19.5.

Hence, the breadth of the rectangle, b = 19.5 cm.

∴ The length and breadth of the rectangle are 21.5 cm and 19.5 cm respectively.

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