Question

the perimeter of a rectangle is numerically equal to its area. if the width of a rectangle is 11\4 cm then its lenghth is

Answer 1

Let the  length of rectangle  be  l and  width be  b ,

b = 11/4

Area  of  rectangle  = l×b

Perimeter  of rectangle = 2(l + b)

Now,

According  to question,

$2(l + b) = l \times b \\  \\   2(l + \frac{11}{4} ) = l \times \frac{11}{4} \\ \\  2l + \frac{11}{2} = \frac{11l}{4} \\  \\ 2l - \frac{11l}{4} = - \frac{11}{2} \\ \\  \frac{8l - 11l}{4} = - \frac{11}{2} \\ \\  - \frac{3l}{4} = - \frac{11}{2} \\ \\  l = - \frac{11}{2} \times - \frac{4}{3} \: \\ \\ l = \frac{22}{3}  \ \  cm$ [/tex]

Answer 2

Given perimeter of rectangle = Area of rectangle and width = 11/4

           2(L+W) = L*W

           2(L + 11/4) = 11L/4

           2L + 11/2 = 11L/4

           11L/4 - 2L = 11/2

           3L/4 = 11/2

            6L = 44

             L = 44/6

             L = 22/3.

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