Question

The area of a rectangle gets reduced by 9 square metres, if it's length is reduced by 5 metres and breadth is increased by 3 metres if we increase the length by 3 metres and the breadth by 2 metres the area increases by 67 square metres . find the length and breadth of the rectangle.​

Answer 1

Correct Question:

The area of a rectangle gets reduced by 9 square metres, if it's length is reduced by 5 metres and breadth is increased by 3 metres. If we increase the length by 3 metres and the breadth by 2 metres ,the area increases by 67 square metres . Find the length and breadth of the rectangle.

Given:-

• The area of a rectangle gets reduced by 9 square metres, if it's length is reduced by 5 metres and breadth is increased by 3 metres.
• If we increase the length by 3 metres and the breadth by 2 metres ,the area increases by 67 square metres.

To find:-

• Length and breadth of the rectangle.

Solution:-

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

Then,

• Area of rectangle = xy m²

★ If its length is reduced by 5 m and breadth is increased by 3 m,

Then,

• Length = (x-5) m
• Breadth = (y+3) m

A/Q, [ 1st case]

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

→ xy+3x-5y-15=xy-9

→ 3x-5y=15-9

→ 3x-5y = 6 .................... [ equation 1 ] ×2

★ If the length is increased by 3 m and the breadth is increased by 2 m,

Then,

• Length = (x+3) m
• Breadth = (y+2) m

A/Q, [ 2nd case]

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

→ xy +2x + 3y +6 = xy + 67

→ 2x+3y = 61................... [ equation 2] × 3

Now,

2 equations will be,

• 6x -10y = 12..........[1]
• 6x + 9y = 183.........[2]

Now subtract eq (1) from eq(2).

6x+9y-6x+10y = 183-12

→ 19y = 171

→ y = 9

• Breadth = 9 m

Now out y=9 in eq(1).

3x-5y=6

→ 3x - 5×9 = 6

→ 3x = 6+45

→ x = 17

• Length = 17 m.

${\underline{\sf{Therefore,\:the\: length\:is\:17\:m\: and\: breadth\:is\:9\:m.}}}$

Answer 2

Answer:

✡ Given ✡

$\leadsto$ The area of a rectangle get reduced by 9m², if length is reduced by 5m and breadth is increased by 3m. If we increase the length by 3m and breadth by 2m, the area is increased by 67m².

✡ To Find ✡

$\leadsto$ What is the length and breadth of the rectangle.

✡ Solution ✡

✏ Let the length of the rectangle be x m

✏And the breadth of the rectangle be y m

$\Rightarrow$ Hence,

➡ Area = Length × Breadth

$\implies$ Area = xy

▶ According to the question,

$\implies$ (x - 5) (y + 3) = xy - 9

$\implies$ x (y + 3) - 5 (y + 3) = xy - 9

$\implies$ xy + 3x - 5y - 15 = xy - 9

$\implies$ xy + 3x - 5y - 15 - xy + 9 = 0

$\implies$ 3x - 5y - 6 = 0 ..... (1)

Again,

$\implies$ (x + 3) (y + 2) = xy + 67

$\implies$ x (y + 2) + 3 (y + 2) = xy + 67

$\implies$ xy + 2x + 3y + 6 = xy + 67

$\implies$ xy + 2x + 3y + 6 - xy - 67 = 0

$\implies$ 2x + 3y - 61 = 0 ..... (2)

Hence, the equation are

$\mapsto$ 3x - 5y - 6 = 0 .... (1)

$\mapsto$ 2x + 3y - 61 = 0 .... (2)

From the equation no 1 we get,

$\implies$ 3x - 5y - 6 = 0

$\implies$ 3x = 6 + 5y

$\implies$ x = $\dfrac{(6 + 5y)}{3}$

Putting the value of x in the equation no (2) we get,

$\implies$ 2x + 3y - 61 = 0

$\implies$ 2$\dfrac{(6+5y)}{3}$ + 3y - 61 = 0

$\implies$ 2(6 + 5y) + 9y - 183 = 0

$\implies$ 12 + 10y + 9y - 183 = 0

$\implies$ 19y - 171 = 0

$\implies$ 19y = 171

$\implies$ y = $\dfrac{171}{19}$

$\implies$ y = 9

Putting the value of x = 9 in the equation no (1) we get,

$\implies$ 3x - 5y - 6 = 0

$\implies$ 3x - 5(9) - 6 = 0

$\implies$ 3x - 45 - 6 = 0

$\implies$ 3x - 51 = 0

$\implies$ 3x = 51

$\implies$ x = $\dfrac{51}{3}$

$\implies$ x = 17

Hence,

$\bigstar$ Length of rectangle = x = 17m

$\bigstar$ Breadth of rectangle = y = 9m

Step-by-step explanation:

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