Question

The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m², what are the length and breadth of the hall?

Answer 1

SOLUTION :  

Given : Area of the floor of the hall : 84 m²

Let the breadth be x m & Length will be = (x + 5) m

A T.Q

Area of rectangle = l × b  

x(x + 5) = 84

x² + 5x = 84

x² + 5x - 84 = 0

x² + 12x - 7x - 84 = 0

[By middle term splitting]

x(x + 12) - 7(x + 12) = 0

(x + 12)(x - 7) = 0

x + 12 = 0 or  x - 7 = 0

x = - 12 or  x = 7

Since , the breadth can't be negative , so x ≠ - 12

Therefore, x = 7

Breadth,b = x = 7 m

Length = (x + 5) = 7 + 5 = 12 m

Hence, the the length of the hall is 12 m and breadth of the hall is 7 m .

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Answer 2

Question :

The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m², what are the length and breadth of the hall?

Solution:

Let the breadth = x

Then length = x+5 m

Area given = 84 m²

Length × Breadth = 84 m²

x×(x+5) = 84 m²

x²+5x = 84 m²

x²+5x-84 = 0

x²-7x+12x-84 = 0

x(x-7)+12(x-7)

(x-7)(x+12) = 0

x = -12

x= 7

But the breadth can't be negative so x = 7.

Breadth = x = 7 m

Length = x+5 = 7+5 = 12 m