Question

If the area of a square of side 84 cm is the same as that of a rectangle of breadth 12 cm, what
is the length of the rectangle?​

Answer 1

$\huge\red{Answer}$→Length, Breath  = 12 , 7  (cm)

             Perimeter  = 38 (cm)

$\huge\green{Explanation}$→

If the longer side is called the length and the length is called  L ; call the breadth  B .

Then we are told:

[1]           B = L + 5 (cm)

and

[2]         B ⋅ L = 84 (sq.cm.)

Substituting   ( L + 5 )  from [1] for  B  in [2]

[3]                   ( L + 5 ) ⋅ L = 84

[4]                    L²+ 5L = 84

[5]                    L ²+5 L− 84 = 0

[6]                   ( L + 12 ) ( L − 7 ) = 0

[7]                   L = − 12             or            L = 7

                      ↑impossible

Since  B = L + 5

          B = 12

Perimeter  = 2 × ( Length + Breadth ) = 2 × ( 7 + 12 ) = 38

$\huge\pink{@alurringbabe}$