Question

the length of a rectangular hall is 5m more than its breadth . if the area of the hall is 594 m. find the perimeter.

Answer 1

Let the breadth of hall be x m.

Then length = (x+5) m

Area of hall = 594 m² ( given )

A/q,

➡ x ( x + 5 ) = 594

➡ x² + 5x = 594

➡ x² + 5x - 594 = 0

➡ x² + 27x - 22x - 594 = 0

➡ x ( x + 27 ) - 22 ( x + 27 )

➡ ( x - 22 ) ( x + 27 )

➡ x = 22 and x = -27

Breadth can't be in -ve, so we will take breadth (x) = 22 m

therefore length = ( x+5 ) = 22+5 = 27 m

Now,

perimeter of rectangle = 2 ( l + b )

➡ 2 ( 27 + 22 )

➡ 2 ( 49 )

➡ 98 m.

Hope it will help you !!!

Answer 2

Solution:

Consider ABCD is a rectangular hall

Take Breadth = x m

Length = (x + 5) m

We know that

Area of rectangular field = l × b

Substituting the values

594 = x (x + 5)

By further calculation

594 = x2 + 5x

0 = x2 + 5x – 594

x2 + 5x – 594 = 0

It can be written as

x2 + 27x – 22x – 594 = 0

Taking out the common terms

x (x + 27) – 22 (x + 27) = 0

So we get

(x – 22) (x + 27) = 0

Here

x – 22 = 0 or x + 27 = 0

We get

x = 22 m or x = -27 which is not possible

We know that

Breadth = 22 m

Length = (x + 5) = 22 + 5 = 27 m

Perimeter = 2 (l + b)

Substituting the values

= 2 (27 + 22)

By further calculation

= 2 × 49

= 98 m

${\fcolorbox{blue}{black}{\blue{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:HumanIntelligence\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}$