Question

the perimeter of a rectangle is 10 meters and its area is 5 1/4 square centimeter what are the length of its sides? solve this using algebra X and Y​

Answer 1

Answer:

• Length = 7/2
• Breadth = 3/2

Explanation:

Given,

Perimeter of a rectangle is 10 metres

Area of the rectangle = 5¼ metres

We need to find the length and breadth.

Let's assume,

• Length = x
• Breadth = y

Then

Perimeter of a rectangle :-

⇒ 2(x + y) = 10

⇒ x + y = 10/2

⇒ x + y = 5 . . . . . . (i)

And, its area = xy = 5¼ . . . . . (ii)

By the identity :-

⇒ (x + y)² - (x - y)² = 4xy

⇒ (x - y)² = (x + y)² - 4xy

From (i) and (ii) :-

⇒ (x - y)² = (5)² - 4(5¼)

⇒ (x - y)² = 25 - 4(21/4)

⇒ (x - y)² = 25 - 21

⇒ (x - y)² = 4

⇒ x - y = √4

⇒ x - y = 2

On solving (i) and (iii) we get,

x + y = 5

x - y = 2

⇒ 2x = 7

⇒ x = 7/2

On substituting ‘x’ in (i) :-

⇒ x + y = 5

⇒ 7/2 + y = 5

⇒ y = 5 - 7/2

⇒ y = 3/2

Hence, the dimensions of the rectangle is

• Length = x = 7/2
• Breadth = y = 3/2

_____________________

Identity used :

• (x + y)² - (x - y)² = 4xy

Formulae :

• Area of a rectangle = length × breadth
• Perimeter of a rectangle = 2(length + breadth)