Perimeter of a rectangle = 2 ( length + breadth )

46 = 2 ( length + breadth )

That is, Length + breadth = 46/2

Length + breadth = 23

length = 23 - breadth

let Length= L and Breadth =B

=> L = 23 - B                                -----(1)

Area is given as 126 meters

Tat is,

L * B = 126                                      -----(2)

Now substitute the value, L= 23 - B in the second equation,

===> ( 23 - B ) * B = 126

Remove the brackets, by multiplying term by term,

===>23 * B - B * B = 126

==> 23B - B^2 = 126

By arranging the terms, we have a quadratic equation here,

====> -B^2 + 23B = 126

Subteract 126 from both sides of the equation,

===> -B^2 + 23B -126 = 126 -126

===> -B^2 + 23B -126 = 0

This is a quadratic equation ( in variable B )

Using quadratic formula, find solutions ( All possible values of B) of the

equation.

Compare the given equation with the standard equation, ax^2 + bx + c = 0.

Then we have,

a = -1 b = 23 and c = -126

We have the quadratic formula,

Here we use the same formula, but for the variable B,

Substitute the values, a, b and c

===>

===>

===>

===> B = (-23 + 5 )/-2 or B = (-23 - 5 )/-2

===> B = (-18 )/-2 or B = (-28 )/-2

===> B = 9 or B = 14

Now, Find out correspopnding values of L

When B = 9,

we have L = 23 - 9 = 14

When B = 14, L = 23 - 14 = 9

So we have two pairs of values,

(Here breadth means width)

Length = 14, breadth = 9

Length = 9 and breadth = 14