Math, asked by kunjalstha999, 2 days ago

b) The area of a rectangular conference hall is 300 m². If the length were decreased by 5 m and the breadth increased by 5 m, the area would be unaltered. Find the length of the room.

Answers

Answered by Itzheartcracer

Answer:

Given :-

The area of a rectangular conference hall is 300 m². If the length were decreased by 5 m and the breadth increased by 5 m, the area would be unaltered.

To Find :-

Length

Solution :-

Let

Length = x

Breadth = y

We know that

Area = Length × Breadth

300 = x × y

300/x = y (1)

Now

According to the question

New length = (x - 5)

New Breadth = (x + 5)

$\sf \: (x - 5)(y + 5) = 300$

$\sf \: (x - 5) \bigg( \dfrac{300 }{x} + 5 \bigg) = 300$

$\sf \: 300 + 5x - \dfrac{15 00}{x} - 25 = 300$

$\sf \cancel{300} + 5x - \dfrac{1500}{x} - 25 = \cancel{300}$

$\sf \: 5x - \dfrac{1500}{x} - 25 = 0$

$\sf \: x \bigg(5x - \dfrac{1500}{x} - 25 \bigg) = 0$

$\sf \: 5 {x}^{2} - 1500 - 25x = 0$

$\sf \: \dfrac{5 {x}^{2} - 1500 - 25x }{5} = \dfrac{0}{5}$

$\sf \: {x}^{2} - 300 - 5x = 0$

$\sf \: {x}^{2} - 5x - 300 = 0$

$\sf \: {x}^{2} - (20x - 15x) - 300 = 0$

$\sf \: {x}^{2} - 20x + 15x - 300 = 0$

$\sf \: x(x - 20) + 15(x - 20) = 0$

$\sf \: (x - 20)(x + 15) = 0$

So, Either

$\sf \: x - 20 = 0$

$\sf \: x = 20$

Or,

$\sf \: x + 15 = 0$

$\sf \: x = - 15$

As length can't be -ve. Hence

Length = 20

Answered by Anonymous