THE LENGTH OF A RECTANGLE IS 4CM LESS THAN THRICE THE WIDTH.WHEN THE LENGTH IS INCREASED BY 7C AND THE WIDTH IS DECREASED BY 2CM,THE PERIMETER EQUALS TO 90CM.FIND THE LENGTH AND WIDTH OF THE RECTANGLE.

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Solution

Let the width = x cm
so length = (3x - 4) cm
perimeter = 2 [x + 3x - 4] = [8x - 8] cm [perimeter of rectangle = 2 (length + breadth)]

WHEN LENGTH IS INCREASED BY 7 CM AND WIDTH DECREASED BY 2CM :

length = (3x - 4) + 7 = [3x + 3] cm
breadth = (x - 2) cm
Perimeter = 2[3x + 3 + x - 2] = 2[ 4x + 1] = (8x + 2) cm
now, 8x + 2 = 90 [given]
$\Rightarrow$ 8x = 88
$\Rightarrow$ x = 11
So width = 11 cm
length = 3(11) - 4 = 33 - 4 = 29 cm

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