Question

164 cm rod is bend to make a rectangle it's length should be 2cm more than three times its breadth what is the length and breadth?

Answer 1

Answer:

We know that the two sides are xx and AxAx , and the perimeter is 2424 , so:

24=2(x+Ax)24=2(x+Ax)

Dividing both sides by 22 :

12=x+Ax12=x+Ax

Subtracting xx from both sides:

12−x=Ax12−x=Ax

Multiplying both sides by xx :

−x2+12x=A−x2+12x=A

Now the maximum/minimum of a quadratic ax2+bx+cax2+bx+c is at x=−b2ax=−b2a , so the best xx would be:

x=−12−2=122=6x=−12−2=122=6

So the maximum area is A=−62+12(6)=−36+72=36A=−62+12(6)=−36+72=36

EDIT: it’s a maximum because A=−x2+12xA=−x2+12x is a downward facing parabola.

Answer 2

Answer:

Length = 60 cm     Breadth = 20 cm

Step-by-step explanation:

164 cm long rod is bent to form rectangle so it means that the perimeter of the rectangle formed is 164 cm

So, Let the breadth of the rectangle = x

      so the length of the rectangle = 2+3x

Perimeter of rectangle = 2( length + breadth )

              164                  = 2( 2 + 3x + x )

              164                  = 2( 2 + 4x )

              164                  = 4 + 8x

              164 - 4             = 8x

              160                  = 8x

                x                    = 160/8

                x                    = 20

So, Breadth = x

                    = 20 cm

Length = 2 + 3x

            = 2 + 3( 20 )

            = 2 + 60

            = 62 cm