Question

here is a rectangle ABCD the length of the rectangle is increased by 10% the width of the rectangle is increased by 5% find the percentage increase in the perimeter of the rectangle

Answer 1

So,first we  know that Square is also a special type of Rectangle,

so consider a Square with side 100 unit ,

Initially                                                                             After increament in                                

                                                                                                        side

Length = 100 unit -(increases by 10% ,So 110% of 100)    NEW length = 110 unit

width = 100 unit (increases by 5% ,So 105% of 100)     NEW  width =     105

initially

Perimeter of Rectangle = 2 x (L + B)  = 2 x (100 +100)

                                                              = 400 unit

After increament in length and width

Perimeter of New Rectangle = 2 x (L + B)  = 2 x (110 +105)

                                                                     = 430 unit.

So we can clearely see that there is an increase of 30 unit in perimeter from initial.

Therefore ,% increase in perimeter will be

                   (final perimeter - initial perimeter)/initial perimeter x 100

                      =  (430 - 400)/400 x 100

                      = 7.5 % increase

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