The area of rectangle room is 80 square.m and if the Length and breadth are increased by 2m then the area would be increased by 40 sq.m .Find the dimensions of the room
Answers
Answer:
area of the rectangle room=80
length increases by 2m
breadth increases by 2m
let lenght be l =2l
breadth be b=2b
area increases by 40cm
then area=120cm
l=b
l+b=80
2L=80
L=80/2
L=40
b=20
2l+2b=120
4(l+b)= 120
l+b=120/4
l+b=30
Answer:
Length = 10 m
Breadth = 8 m
Step-by-step explanation:
Let the length of the room be 'l', and the breadth of the room be 'b'.
A/q,
l*b = 80 m² ...(i)
When the length and the breadth of the room are increased by 2 m, the area increases by 40 m².
(l+2)(b+2) = (80+40) m²
⇒l*b+2l+2b+4 = 120 m²
⇒l*b+2(l+b)+4 = 120 ...(ii)
Subtracting (i) from (ii):
l*b + 2(l+b) + 4 = 120
-
l*b = 80
----------------------------------
2(l+b) + 4 = 40
⇒2(l+b) = 36
⇒l+b = 18
⇒l = 18-b ...(iii)
Putting l = 18-b in (i):
b(18-b) = 80
⇒18b-b² = 80
⇒b²-18b+80 = 0
⇒b²-10b-8b+80 = 0
⇒b(b-10)-8(b-10) = 0
⇒(b-10)(b-8) = 0
⇒b=10 or b=8
Putting these values of 'b' in (iii):
If b=10,
l = 18-10 = 8
If b=8,
l = 18-8 = 10
But we know that the length is always longer than the breadth.
So, the length of the rectangular room is 10 m and the breadth of that room is 8 m.