Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 64 of Exercise 10E
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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.
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
minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.
