Question

lf the length of a rectangle is decreased by 2 m and the breadth increased by 2 m the area would increase 8 square metre . If the length is decreased by 3m and the breadth decreased by 1m the area would decrease by 27 square metre. What are the length and breadth ?

Radhe Radhe


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Answer 1

Answer:

It is given that in a rectangle, when the length is increased and breadth is reduced each by 2 units, the area reduces by 28 square units and when the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units, so by using this we can make two different equations.

For which, let the length of the rectangle be x units and the breadth be y units.It is given that in a rectangle, when the length is increased and breadth is reduced each by 2 units, the area reduces by 28 square units and when the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units, so by using this we can make two different equations.

For which, let the length of the rectangle be x units and the breadth be y units.

We know that,

Area of the rectangle = Length × Breadth

=x×y

=xy sq. units

Now, we will make equations from the given information.Now, we will make equations from the given information.

(x+2)×(y−2)=xy−28……… (1)

and, (x−1)×(y+2)=xy+33……... (2)

Taking equation (1),

(x+2)×(y−2)=xy−28

⇒xy−2x+2y−4=xy−28⇒−2x+2y=−28+4⇒−2x+2y=−24⇒2(−x+y)=−24⇒−x+y=−242⇒−x+y=−12⇒x=y+12 ………… (i)

Now, taking equation (2),

(x−1)×(y+2)=xy+33

⇒xy+2x−y−2=xy+33⇒2x−y−2=33⇒2x−y=33+2

⇒2x−y=35 ………… (ii)

Substituting equation (i) in equation (ii), we get,

2(y+12)−y=35⇒2y+24−y=35⇒y+24=35⇒y=35−24⇒y=11

Now, substituting y=11 in equation (i), we obtain

x=11+12⇒x=23

Therefore, length of the rectangle =x=23units

and breadth of the rectangle Hence, area of the rectangle =Length ×Breadth

=x×y=23×11=253 square units.

∴ Area of the rectangle is 253 square units.

Note – A rectangle is a quadrilateral with four straight sides and four right angles. It has unequal adjacent sides, in contrast to a square. These kinds of questions are very simple and easy to solve if one understands the question properly and knows all the basic formulas.

Hope it helps you keep smiling :)

Answer 2

$\mathfrak\pink{Answer}$

length = 12 m, breath = 6m

$\mathfrak\orange{step \: by \: step \: exapanation:-}$

Let length be x. and if the length of a rectangle is decreased by 2m then,

(x-2)

Let breadth be y and if breadth increase

2m,(y+2)

then,area =(length breadth)

(x - 2)(y + 2) = xy + 8sqm

x(y + 2) - 2(y + 2) = xy + 8

xy + 2x - 2y - 4 = xy + 8

xy + 2x - 2y - 4 = xy + 8

xy + 2x - 2y = xy + 8 + 4

xy + 2x - 2y = xy + 12

xy + 2x - 2y - xy = 12

2x - 2y = 12

x - y = 6

x=6+y. (1)

Again if length is decreased by 3m and breadth is decreased by 1 m the area would be decreased by27 square m

then,

(x - 3)(y - 1) = xy - 27

x(y - 1) - 3(y - 1) = xy - 27

xy - x - 3y + 3 = xy - 27

(x - 3)(y - 1) = xy - 27

x(y - 1) - 3(y - 1) = xy - 27

xy - x - 3y + 3 = xy - 27

xy-x-3y+3-xy+27 - x - 3y + 3 + 27 = 0

- x - 3y + 30 = 0

- x = 3y - 30

- (6 + y) = 3y - 30

=-6-y=3y-30

- 6 + 30 = 3y + y

24 = 4y

24/4 = y

=6=y

y = 6m

now putting the value of y in the equation

(1)

x = 6 + y

x = 6 + 6

x = 12m

therefore length =12m and breadth=6m