Question

Find the length and breadth of a room, if its area is 120 m² and perimeter 44m.​

Answer 1

Answer:

Let the sides of our rectangle be “a” and “b”.

The perimeter of a triangle = sum of the lengths of its side = 2a + 2b.

Area of a rectangle = length * breadth

= ab.

Perimeter = 2a + 2b = 44. Which implies that,

a + b = 22.

Area = ab = 120.

And we know,

(a - b)^2 = (a + b)^2 - 4ab

From this if we calculate the value of a - b, we can figure out the value of “a” and “b”.

(a - b)^2 = (22)^2 - 4*120

= 484 - 480 = 4.

Which implies that,

a - b = 2, or a - b = - 2.

{ Doesn't really matter because I had not defined which one is length and breadth in “a” and “b” and so their values are interchangeable }

And we had found out before that,

a + b = 22, through our perimeter.

If we solve these two equations, we get,

a = 12, b = 10.

Which is our answer