A room 5m long and 4m wide is surrounded by a verandah . If the verandah occupies an area of 22 square m , find the width of the verandah.Pieas give the ans with detailed steps.
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Answered by
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The area of the room= 5×4 = 20 sq. m
Let the width be x.
Then,
(5+2x)(4+2x) - 22 = 20
or, 20 + 18x + 4x^2 -42 = 0
or, 4x^2 + 18x - 22 = 0
or, 2x^2 + 9x - 11 = 0
or, 2x^2 -2x +11x - 11 =0
or, 2x(x - 1) +11(x - 1) = 0
or, (x - 1)(2x + 11) = 0
From the above relation,
x = 1 or x = -11/2
negative answer cannot be accepted as a measure of width.
so, x = 1
The width of the verandah is 1 m.
As the verandah is surrounding the room, it increases both the length and the width two times by the value of its width.
And, the total area of the room and the verandah = area of the room + area of the verandah
Let the width be x.
Then,
(5+2x)(4+2x) - 22 = 20
or, 20 + 18x + 4x^2 -42 = 0
or, 4x^2 + 18x - 22 = 0
or, 2x^2 + 9x - 11 = 0
or, 2x^2 -2x +11x - 11 =0
or, 2x(x - 1) +11(x - 1) = 0
or, (x - 1)(2x + 11) = 0
From the above relation,
x = 1 or x = -11/2
negative answer cannot be accepted as a measure of width.
so, x = 1
The width of the verandah is 1 m.
As the verandah is surrounding the room, it increases both the length and the width two times by the value of its width.
And, the total area of the room and the verandah = area of the room + area of the verandah
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68
Answer:
Step-by-step explanation:
2 answers · Mathematics
Best Answer
Let the width be x m
Outer area = ( 5 + 2x ) ( 4 +2x )
Inner Area = 5 X 4 = 20
Area of verandah = ( 5 + 2x ) ( 4 + 2x) - 20 = 22 m^2
20 + 8x + 10x + 4x^2 - 20 = 22
4x^2 +18x - 22 = 0
2x^2 +9x - 11 = 0
2x^2 -2x +11x - 11 = 0
2x ( x -1) + 11( x-1) = 0
( 2x +11) ( x-1) = 0
Rejecting the negative value , x = 1
ANSWER 1 meter
CHECK
7 X 6 = 42
5 X 4 = 20
SUBTRACT = 22 m^
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