Question

the area if rectangular room is 45sq.m. if the length had been 3m less and the breadth 1m more,it would have been square find the length of the room

Answer 1

Answer:9cm

Step-by-step explanation:

Length (l), breadth (b)

Or, l*b = 45

So, l =  

45

b

45b

….(i)

Or, l – 3 = b + 1

Or, l – b = 4….(ii)

Or,  

45

b

−b=4

45b−b=4

Or,  

45−

b

2

b

=4

45−b2b=4

Or, 45 – b2 = 4b

Or, b2 + 4b – 45 = 0

Or, b2 + 9b – 5b – 45 = 0

Or, b(b – 5) + 9(b – 5) = 0

Or, (b – 5)(b + 9) = 0

So, b = 5, -9.

So, b = 5cm

Now,

Or, l – b = 4

Or, l – 5 = 4

So, l = 9cm

Answer 2

Answer:

given,

area of the rectangular room, A=45

let,

length=a

breadth=b

so,

$area = 45 \\ > ab = 45$

by the 2nd condition,

$a - 3 = b + 1 \\ > a = b + 4$

now,

$ab = 45 \\ > (b + 4)b = 45 \\ > {b}^{2} + 4b = 45 \\ > {b}^{2} + 4b - 45 = 0 \\ > {b}^{2} + 9b - 5b - 45 = 0 \\ > b(b + 9) - 5(b + 9) = 0 \\ > (b + 9)(b - 5) = 0 \\ \\ either \\ b + 9 = 0 \\ > b = - 9 \: (not \: acceptable \: as \: length \: cant \: be \: negative) \\ or \\ b - 5 = 0 \\ > b = 5$

so, breadth of the room=5 m

therefore, length of the room=45/5=9 m

length=9, breadth=5