Question

The dimensions of the rectangular box are in the ratio 4: 3 and its height is 5.5 m. the cost of the decoratingits walls [including doors and windows] at 6.60 rupees at metre square is Rs 5082. find the length and breadth of the room

Answer 1

Answer :

Given : The dimensions of the rectangular box are in the ratio 4: 3 and its height is 5.5 m.

Let ratio coefficient = x , Then

Length of room = 4x
And
Breadth of room = 3x

And Also given : The cost of the decorating walls [including doors and windows] at 6.60 rupees at metre square is Rs 5082.
So,
Total surface area $\times$ Rate of decorating = 5082

2 ( Length $\times$ Breadth + Length $\times$ Height + Breadth $\times$ Height ) $\times$ 6.60 = 5082

13. 2 ( 4x $\times$ 3x + 4x $\times$ 5.5 + 3x $\times$ 5.5 ) = 5082

12x² + 22x + 16.5x = $\frac{5082}{13.2}$

12x² + 38.5x = 385

12x² + 38.5x - 385 = 0

We know quadratic formula

x = $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ Here a = 12 , b = 38.5 , c = -385 , So

x = $\frac{-38.5\pm \sqrt{{\left(38.5\right)}^2-4\times 12\times \left(-385\right)}}{2\times 12}=\frac{-38.5\pm \sqrt{1482.25+18480}}{24}=\frac{-38.5\pm \sqrt{19962.25}}{24}=\frac{-38.5\pm 141.28}{24}$
So,
x = $\frac{-38.5+141.28}{24}=\frac{102.78}{24}=4.2825$
And
x = $\frac{-38.5-141.28}{24}=-\frac{179.78}{24}=-7.4908$

Here Our length and breadth of room = 4x and 3x , So value of x can't be negative , So We neglect x = - 7.4908 And take

x = 4.2825

Then

Length of room = 4x = 4 $\times$ 4.2825 = 17.13 m
And
Breadth of room = 3x = 3 $\times$ 4.2825 = 12.8475 m = 12.85 m ( Ans )