Question

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Answer 1

Solution -

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

Then,

Area of the rectangle =l×b = xy sq. units.

If length is reduced by 5 units and the breadth is increased by 3 units, then area is reduced by 9 square units.

∴xy−9=(x−5)(y+3)

⇒xy−9=xy+3x−5y−15

⇒3x−5y−6=0

When length is increased by 3 units and breadth by 2 units, the area is increased by 67 sq. units.

∴xy+67=(x+3)(y+2)

⇒xy+67=xy+2x+3y+6

⇒2x+3y−61=0

Thus, we get the following system of linear equations:

3x−5y−6=0...... 1)

And,

2x+3y−61=0

$2x = 61 - 3y$

$x = \frac{61 - 3y}{2} ......2)$

By substituting the value of x in equation 1) we will get -

$3 \times \frac{61 - 3y}{2} - 5y - 6 = 0$

$\frac{183 - 9y}{2} - 5y - 6 = 0$

$\frac{183 - 9y - 10y}{2} = 6$

$183 - 19y = 12$

$19y = 183 - 12$

$19y = 171$

$y = \frac{171}{19}$

$y = 9$

Now, substituting the value of y in equation 2) we will get -

$x = \frac{61 - 3 \times 9}{2}$

$x = \frac{61 - 27}{2}$

$x = \frac{34}{2}$

$x = 17$

Therefore the length of rectangle is 17 units and breadth of the rectangle is 9 units.

Answer 2

Step-by-step explanation:

length = 17 cm

breath = 9 cm