a floor is 10cm long and 8cm wide. it is surrounded by an uniform width verandah all around from outside.if the area of verandah is 40 square m.Then find the width of the varandah
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2
let the width of the veranda be x
of the rectangle without veranda:-
area = 10 x 8 = 80
of the rectangle with veranda:-
length = 10+2x
breadth = 8 + 2x
area = (10+ 2x )(8 + 2x )
= 80 + 20x + 16x + 4x^2
= 4x^2 + 36x + 80
now
area of the veranda = 40
area of the floor with veranda
- area of floor without veranda = 40
4x^2 + 36x + 80 - 80 = 40
4x^2 +36x -40 = 0
x^2 + 9x - 10 =0
x^2 + 10x- x - 10 = 0
x ( x + 10) - (x + 10) = 0
(x - 1)(x + 10) = 0
therefore
either
x-1 = 0
x = 1
or
x+10 = 0
x = -10
since width cannot be negative.
so
x = 1
the width of the veranda = 1m sq
of the rectangle without veranda:-
area = 10 x 8 = 80
of the rectangle with veranda:-
length = 10+2x
breadth = 8 + 2x
area = (10+ 2x )(8 + 2x )
= 80 + 20x + 16x + 4x^2
= 4x^2 + 36x + 80
now
area of the veranda = 40
area of the floor with veranda
- area of floor without veranda = 40
4x^2 + 36x + 80 - 80 = 40
4x^2 +36x -40 = 0
x^2 + 9x - 10 =0
x^2 + 10x- x - 10 = 0
x ( x + 10) - (x + 10) = 0
(x - 1)(x + 10) = 0
therefore
either
x-1 = 0
x = 1
or
x+10 = 0
x = -10
since width cannot be negative.
so
x = 1
the width of the veranda = 1m sq
joe30:
so taking roots of the equation
x=1 and x= -10
yes
x= -10 not possible since quantity is lengtg
length
hence directly you gotta take x=1
yes
hey maria how u took the length same
cause acc to question its not said its same in both
there its written floor is surrounded all round by verandah.
Answered by
0
check out this..but I'm not sure okk.
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ok
how did u get length 1p
10
the floor's length is 10 m its given.
so how u made it length of the verandah.
cause in ques its written verandah surrounding floor all around.
so diagram will be of two rectangles..bigger rectangle of whole including the floor.
and smaller rectangle inside the bigger one of only floor.
i didn't understand what u want to say
I'm asking her..uhh u make a diag acc to the info of the ques..u will understand
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