Question

The area of a rectangle is reduced by 14 meter square if length is increased by 2 meter and breadth reduced by 2 meter area increased by 15 meter square if length reduced by 4 meter breadth increasing by 5 meter find dimensions of the rectangle​

Answer 1

Answer:

Let the length of the rectangle be x metres and the breadth be y metres.

Area of the rectangle=length×breadth

=x×y=xy sq. metres

From the given information, we have,

(x+3)×(y−4)=xy−67

and(x−1)×(y+4)=xy+89

(x+3)×(y−4)=xy−67

=>xy−4x+3y−12=xy−67

=>4x−3y=55

=>4x=3y+55....(i)

Also,(x−1)×(y+4)=xy+89

=>xy+4x−y−4=xy+89

=>4x−y=93....(ii)

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

4x−y=93

=>3y+55−y=93

=>2y=38

=>y=19

Substituting y=19 in equation (i), we get,

4x=3y+55

=>4x=3(19)+55

=>4x=112

=>x=28

Therefore, length of rectangle =x=28 metres

breadth of rectangle =y=19 metres

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that

Length of rectangle = x meter

Breadth of rectangle = y meter.

So, Area of rectangle = xy m²

According to first condition,

The area of a rectangle is reduced by 14 meter square if length is increased by 2 meter and breadth reduced by 2 meter.

Mathematically,

Length of rectangle = x + 2

Breadth of rectangle = y - 2

Area of rectangle = xy - 14

So,

$\rm :\longmapsto\:(x + 2)(y - 2) = xy - 14$

$\rm :\longmapsto\:xy - 2x + 2y - 4 = xy - 14$

$\rm :\longmapsto\: - 2x + 2y - 4 + 14 = 0$

$\rm :\longmapsto\: - 2x + 2y + 10 = 0$

$\rm :\longmapsto\: - 2(x - y - 5) = 0$

$\rm :\longmapsto\: x - y - 5= 0$

$\rm :\longmapsto\:x - y = 5 - - - (1)$

According to second condition,

Area increased by 15 meter square, if length reduced by 4 meter and breadth increased by 5 meter.

Mathematically,

Length of rectangle = x - 4

Breadth of rectangle = y + 5

Area of rectangle = xy + 15

$\rm :\longmapsto\:(x - 4)(y + 5) = xy + 15$

$\rm :\longmapsto\:xy + 5x - 4y - 20 = xy + 15$

$\rm :\longmapsto\:5x - 4y - 20 - 15 = 0$

$\rm :\longmapsto\:5x - 4y - 35 = 0$

$\rm :\longmapsto\:5x - 4y = 35 - - - - (2)$

Multiply equation (1) by 5, we get

$\rm :\longmapsto\:5x - 5y = 25 - - - (3)$

On Subtracting equation (3) from equation (2), we get

$\rm :\longmapsto\:y = 10$

On substituting the value of y in equation (1), we get

$\rm :\longmapsto\:x - 10 = 5$

$\rm :\longmapsto\:x = 5 + 10$

$\rm :\longmapsto\:x = 15$

Hence,

Length of rectangle, x = 15 meter.

Breadth of rectangle, y = 10 meter.