Question

e length of the floor of a rectangular hall is 10m more than its breadth. If 34 carpets of size 6×4m are required to cover the floor of the hall then find the length and breadth of the hall.

Answer 1

Given:

The length of the floor of a rectangular hall is 10m more than its breadth. If 34 carpets of size 6×4m are required to cover the floor of the hall then find the length and breadth of the hall.

To find:

The length and breadth of the hall.

Solution:

Let,

"b" be the breadth of the floor of the rectangular hall

"l" be the length of the floor of the rectangular hall

The length of the floor of a rectangular hall is 10m more than its breadth, so we get

$l = b + 10\: .\:.\:.\:(1)$

The length of the carpet = 6 m

The breadth of the carpet = 4 m

No. of carpets used to cover the floor of the hall = 34

∴ The total area of the 34 carpets will be,

= 34 × 6 × 4 . . .  [∵ area of a rectangle = length × breadth]

= 816 m²

Now, we know,

Area of the floor of the rectangular hall = Area of 34 carpets

$\implies l\times b = 816$

on substituting from (1)

$\implies (b+10)\times b = 816$

$\implies b^2 + 10b = 816$

$\implies b^2 + 10b - 816 = 0$

$\implies b^2 + 34b - 24b - 816 = 0$

$\implies b(b + 34) - 24(b + 34) = 0$

$\implies (b + 34)(b - 24) = 0$

$\implies b = -34 \:or\:b = 24$

the measurement of the floor cannot be negative, so discarding the negative value

$\implies \bold{b = 24\:m}$

∴ $\bold{l} = b +10 = 24 + 10 = \bold{34\:m}$

Thus, the length and breadth of the hall are 34 m and 24 m respectively.

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Answer 2

Answer:

Step-by-step explanation: