Question

Find the dimensions of a rectangle with a perimeter of 112 cm if the length is 4 cm less than four times the width.

Answer 1

Solution :
                 Perimeter of rectangle = 112 cm    ----------------- (1st EQUATION)
               let the width of rectangle be x cm
               therefore length of rectangle = 4x - 4
We know that ,
         Perimeter of rectangle = 2(length + width)
                                         = 2 (4x - 4 + x)
                                         =2 (5x - 4)
                                         = 2*5x - 2*4
                                         =10x - 8      ------------- (2nd equation)
From 1st and 2nd we get ,
                         112 = 10x - 8
                       or 112 +8 = 10x
                       or 120 = 10x 
                       or 120/10 =x
                     or 12 = x
                     or x =12
hence width of rectangle = 12 cm
therefore , length of rectangle = 4x - 4 = 4*12 - 4 = 48 - 4 = 44 cm

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