Question

area of rectangle is 21 metre square if the perimeter of the rectangle is 20 find the length and breadth of the rectangle. ​

Answer 1

Step-by-step explanation:

this is complete solution for this sum.

Answer 2

The length and breadth of the rectangle are 7m and 3m respectively.

We know that for a rectangle of length 'l' and breadth 'b', its area is given as lb

Similarly, its perimeter is given as 2(l+b)

Given, the area of the rectangle is 21 m²

So, lb = 21

⇒l = 21/b            ...(1)

And, permineter = 20m

So, 2(l+b) = 20

⇒(l+b) = 10              ...(2)

Putting l = 21/b from (1) in (2),we get:

21/b + b = 10

Mutiplying with 'b' on both sides, we get:

21 + b² = 10b

⇒ b² - 10b + 21 = 0

⇒ b²  - 7b - 3b + 21 = 0

⇒ b(b-7) - 3(b-7) = 0

⇒ (b-7)(b-3) = 0

By zero product rule,

When b = 7m

l = 10 - b = 3 m

This is absurd because, we know that length of a rectangle cannot be less than its breadth.

So, breadth = 3m

and, length = 10 - 3 = 7m