Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 61 of Exercise 10E
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The perimeter of a rectangular plot is 62 m and its area is 228 sq meters. Find the dimensions of the plot.
Let the length and breadth of rectangular plot be x and y respectively.
Perimeter = 2(x + y) = 62 – – – – – (1)
Area = xy = 228
y = 228/x
Putting the value of y in 1
taking LCM
x2 + 228 = 31x cross multiplying
x2 – 31x + 288 = 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 = – 31 c = 288
= 1.288 = 288
And either of their sum or difference = b
= – 31
Thus the two terms are – 19 and – 12
Difference = – 19 – 12 = – 31
Product = – 19. – 12 = 288
x2 – 19x – 12x + 288 = 0
x(x – 19) – 12(x – 19) = 0
(x – 19) (x – 12) = 0
x = 19 or x = 12
if x = 19
if x = 12
length is 19m and breadth is 12m
length is 12m and breadth is 19m
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.
