Q. 645.0( 4 Votes )

The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. Their areas being equal, find their dimensions.

Answer :

Let the breadth of a rectangle be x cm

According to the question;


Side of square = (x + 4) cm


Length of a rectangle = [3(x + 4)] cm


Area of rectangle and square are equal – –


3(x + 4)x = (x + 4)2


3x2 + 12x = (x + 4)2


3x2 + 12x = x2 + 8x + 16 { using (a + b)2 = a2 + 2ab + b2}


2x2 + 4x – 16 = 0


x2 + 2x – 8 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 2 c = – 8


= 1. – 8 = – 8


And either of their sum or difference = b


= 2


Thus the two terms are 4 and – 2


Difference = 4 – 2 = 2


Product = 4. – 2 = – 8


x2 + 4x – 2x – 8 = 0


x(x + 4) – 2(x + 4) = 0


(x + 4) (x – 2) = 0


x = – 4 or x = 2


x = 2 (width cannot be negative)


Thus the breadth of a rectangle = 2 cm


Length of a rectangle = [3(x + 4)] = 3(2 + 4) = 18 cm


Side of square = (x + 4) = 2 + 4 = 6cm


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