Question

the length of room exceed its breath by 30cm if the lenght is increased by 30 cm and the breadth is decreased by 20cm ,the area remain same.Find the length and breadth of the room​

Answer 1

Answer:

$Breadth = x$

$Length = x + 30$

$Area = x(x + 30)$

According to Question:-

When the length is increased by 30 cm and the breadth is decreased by 20 cm, the area will remain same.

$Breadth = x - 20$

$Length = (x + 30) + 30 \\= x + 60$

$Area = (x - 20)(x + 60)$

Solution:-

If both the areas are equal, then:-

$x(x + 30) = (x - 20)(x + 60)$

$x^{2} + 30x = x(x + 60) - 20(x + 60)$

$x^{2} + 30x =x^{2} + 60x - 20x - 1200$

$x^{2} + 30x = x^{2} + 40x - 1200$

$x^{2} -x^{2} = 40x - 1200 - 30x$

$0 = 10x - 1200$

$1200 = 10x$

$\frac{1200}{10} = x$

$120 = x$

Breadth = 120 cm

Length = x + 30

= 120 + 30

= 150 cm

Verify:-

Breadth = 120 cm

Length = 150 cm

Revised breadth = 120 - 20

= 100 cm

Revised length = 150 + 30

= 180 cm

$120 * 150 = 100 * 180$

$18000 = 18000$

LHS = RHS

Hence, verified

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Answer 2

Answer:

Answer in attachment..

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