Question

The area of a rectangle gets reduced by 8 m2, when its length is reduced by 5m and its breadth is increased by 3 m. If we increase the length by 3 m and breadth by 2 m, the area is increased by 74 m2. Find the length and the breadth of the rectangle.

Answer 1

Answer:

Step-by-step explanation:

A.T.Q

Area of rectangle=xy-8

Length of rectangle =x-5

Breadth of rectangle=y+3

therefore,

Area of rectangle =l(b)

=xy-8=x-5(y+3)

=xy-8=xy+3x-5y-15

=xy-8+15=xy+3x-5y

=3x-5y=7.................(1)

xy+74=x+3(y+2)

xy+74=xy+2x+3y+6

2x+3y=68.................(2)

multiply eq (1)with 2and eq (2)with 3 for equilibrium,and subtract .

6x-10y=14

-6x+9y=204

    subtracted value=-19y=-190

                       y=190/19=10

therefore,   substituting the value of y in eq (1)

then we get ,

3x-5(10)=7

3x-50=7

3x=57

x=57/3

x=19

Answer 2

Answer:

Given:

The area of rectangle gets reduced by 8m², If its length

is reduced by 5m and breadth is increased by 3m. If we increased length by 3m and breadth by 2m, the area is increased by 74m².

To find:

The length and breadth of the rectangle and their area.

Explanation

:

Let the length of the rectangle be R &

Let the breadth of the rectangle be M.

We know that area of rectangle: Length × Breadth [sq. units]

∴ Area = RM

According to the question:

When the length is reduced by 5m and breadth is increased by 3m;

New length= (R-5)m

New breadth= (M+3)m

New area= (R-5)(M+3)m²

Therefore,

→ RM - (R-5)(M+3)=8

→ RM - [RM+3R -5M -15]=8

→RM -RM -3R +5M +15=8

→ 0 -3R +5M +15=8

→ 3R -5M =15-8

→ 3R -5M =7..............................(1)

&

When the length is increased by 3m and breadth is increased by 2m;

New length= (R+3)m

New breadth= (M+2)m

New area= (R+3)(M+2)m²

→ (R+3)(M+2)- RM= 74

→ RM +2R +3M+6- RM =74

→ RM -RM +2R +3M+6=74

→ 0 +2R+3M +6=74

→ 2R +3M = 74- 6

→ 2R +3M= 68............................(2)

Using Substitution Method:

From equation (1), we get;

⇒ 3R -5M =7

⇒ 3R =7+5M

⇒ R= 7+5M/3 ............................(3)

Putting the value of R in equation (2), we get;

$⇒2( \frac{7 + 5M}{3} ) +3M =68$

$⇒ \frac{14 + 10M}{3} + 3M = 68$

⇒ 14 +10M +9M= 204

⇒ 14 + 19M =204

⇒ 19M =204 -14

⇒ 19M = 190

$⇒ M= \cancel{\frac{190}{19} }m </p><p>$

⇒ M= 10m

Now,

Putting the value of M in equation (3), we get;

$⇒ R= \frac{7+5(10)}{3} </p><p>$

$⇒ R= \frac{7+50}{3} </p><p>$

$⇒ R= \cancel{\frac{57}{3}}$

⇒ R= 19m

Hence,

The length of the rectangle,R=19m

The breadth of the rectangle,M=10m

Area of the rectangle:

→ Length × Breadth

→ 19m × 10m

→ 190m².