Question

if the lenght of a rectangle increased by 5 m and breadth decreased by 3m the area would decreased by 5 square meters .if the lenght increased by 3m and breadth increased by 2m the area would increased by 50 square m. what are the length and breadth​

Answer 1

Answer:

Let length and breadth of a rectangle is x and y. Then, as per first condition,

(x-5)(y+3)=xy-9

=> xy-5y+3x-15=xy-9

=> 3x-5y=6 .....(i)

As per second condition,

(x+3)(y+2)=xy+67

=> xy+3y+2x+6=xy+67

=> 2x + 3y = 61 .....(ii)

On multiplying Eq. (i) by 3 and Eq. (ii) by 5 then adding, we get

9x - 15y = 18

10x + 15y = 305

----------------

=> 19x = 323

=> x = 3231932319=17

Hence, the length of rectangle is 17 m

Answer 2

Question :–

If the lenght of a rectangle increased by 5 m and breadth decreased by 3m the area would decreased by 5 square meters .if the lenght increased by 3m and breadth increased by 2m the area would increased by 50 square m. what are the length and breadth ?

Answer :–

• Length = 10
• Breadth = 8

Solution :–

Let, the length be l and breadth be b.

So,

Area = l × b

ATQ,

● Length is increased by 5m so,

→ l + 5

● Breadth is decreased by 3m so,

→ b - 3

Now, the area will be :–

→ (l + 5)(b - 3)

→ lb - 5

$lb - 3l + 5b - 15 = lb - 5$

$\boxed{ \sf \red{ - 3l + 5b = 10}}........(1)$

Again,

● Length is increased by 3m.

● Breadth is increased by 2m.

● Area will increase by 50m.

$(l + 3)(b + 2) = lb + 50$

$lb + 2l + 3b + 6 = lb + 50$

$\boxed{ \sf \red{2l + 3b = 44}}.........(2)$

Multiply equation (1) from 2 & equation (2) from 3.

→ -6l + 10b = 20

→ 6l + 9b = 132

Now, Adding the both equation s :–

→ (-6l) + 6l + 10b + 9b = 20 + 132

→ 0l + 19b = 152

→ 19b = 152

→ b = 152/19

→ b = 8

Now, substitute the b in equation (2) :–

2l + 3(8) = 44

2l + 24 = 44

2l = 44 - 24

2l = 20

l = 20/2

l = 10

Hence,

1. The length is 10m.
2. The breadth is 8m.