Question

14)
(c) The area of rectangle gets reduced by 8 m2, if its length is reduced by 5m
and breadth is increased by 3 m. If we increased length by 3 m and breadth
by 2m, the area is increased by 74 m. Find the length and breadth of the
rectangle. Also find its area.



​

Answer 1

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

A.T.Q,

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

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

3x - 5y = 7 --------(i)

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

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

2x + 3y = 68 ---------(ii)

Multiplying eq.(i) by 2 and eq.(ii) by 3 we have

6x - 10y = 14

6x + 9y = 204

-------------------------- Subtract

-19y = -190

19y = 190

[ y = 10 ]

Putting value of y in eq(i) , we have

3x - 5(10) = 7

3x = 57

x = 57/3 or 19

[ x = 19 ]

Area of rectangle = xy

=> 19 × 10

=> 190 m²

Hence , Length of rectangle is 19 m and breadth of rectangle is 10 m

Answer 2

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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= $\frac{7+5M}{3}$............................(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= $\cancel{\frac{190}{19} }m$

⇒ M= 10m

Now,

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

⇒ R= $\frac{7+5(10)}{3}$

⇒ R= $\frac{7+50}{3}$

⇒ R= $\cancel{\frac{57}{3}} m$

⇒ 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.