## Book: RS Aggarwal - Mathematics

#### Subject: Maths - Class 10th

##### Q. No. 61 of Exercise 10E

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61
##### 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

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