The width of a card is 3 centimeters shorter than the length. The area is 46.75 square centimeters. What is the perimeter?

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Answer 1 · 2017-02-01T09:07:10

Perimeter is #40# #cm.#

Let the length be #x# #cm.# Ten width is #(x-3)# #cm# and as area of card is #46.75# #cm^2#.

Hence #x(x-3)=46.75# or #x^2-3x=46.75# and multiplying by #4#, we get

#4x^2-12x=187#

or #4x^2-12x-187=0#

i.e. #4x^2-34x+22x-187=0#

i.e. #2x(2x-17)+11(2x-17)=0#

i.e #(2x+11)(2x-17)=0#

As #2x+11# cannot be zero, we have #2x-17=0# i.e. #x=17/2=8.5#

Hence length is #8.5# and width is #11.5-3=8.5#

and perimeter is #2xx(11.5+8.5)=2xx20=40# #cm.#