Question

A prayer hall having floor area 300 m is to be constructed. Its length has to be
one meter more than twice its breadth. Present this problem mathematically in the
form of a quadratic equation and hence find the dimensions of the floor of the hall.
(Use factorisation method for solving the quadratic equation).​

Answer 1

Answer:

Step-by-step explanation:

Area of rectangle = l * b

Let Breadth is x,

So as length is twice  and 1 meter more than breadth

So length will be (1 + 2x)

Area of rectangle = l * b

300 = x (1+ 2x)

300 = x + 2$x^{2}$

2$x^{2}$ + x - 300 = 0

2$x^{2}$ + 25x - 24x - 300 = 0

x (2x + 25) - 12(2x + 25) = 0

(x-12) (2x+25) = 0

x-12 = 0 ; 2x + 25 =0

x = 12 ; x = -25/2

We neglect -25/2 as any length can't be in minus

So x = 12

Breadth = x= 12

Length = (1 + 2x) = (1+ 2*12)

= (1 + 24)

= 25 m

Answer 2

✬ Length = 25 m ✬

✬ Breadth = 12 m ✬

Step-by-step explanation:

Given:

• Area of floor of prayer hall is 300 m².
• Length of hall is 1 m more than twice the breadth.

To Find:

• What are the dimensions of prayer hall?

Solution: Let the breadth of prayer hall be b m. Therefore,

➟ Length of hall = 1 more than twice b

➟ Length = (2x + 1)m

As we know that

★Area of Rectangle = Length $\times$Breadth★

A/q

$\implies{\rm }$ 300 = (2x + 1)(x)

$\implies{\rm }$ 300 = 2x² + x

$\implies{\rm }$ 0 = 2x² + x – 300

Now, by the method of middle term splitting

➙ 2x² + x – 300

➙ 2x² – 24x + 25x – 300

➙ 2x (x – 12) + 25 (x – 12)

➙ (2x + 25) (x – 12)

➙ 2x + 25 = 0 or, x – 12 = 0

➙ x = –25/2 or x = 12

Take the positive value of x. { Negative ignored }

So,

➱ Breadth of prayer hall is x = 12 m

➱ Length of hall = (2x + 1)

=> 2(12) + 1 = 25 m