Question

2. Length of a floor is 4 metre more than its breadth. If both the length and breadth are
increased by 1 metre each the area increases by 27 square metre. Find the length and
breadth of the floor. Also find the area of the floor.
(Ans. Length = 15 m, Breadth = 11 m, Area
Breadth = 11 m, Area = 165 sq. m)​

Answer 1

Required Answer:-

Let the length be l and the breadth be b.

According to question,

➙ Length = Breadth + 4

➙ l = b + 4

➙ l - b = 4 --------(1)

Now, A change was made which increased the area by 27 m². Initially the area will be lb and now it will be (l + 1)(b + 1).

Then,

➙ (l + 1)(b + 1) = lb + 27

➙ lb + l + b + 1 = lb + 27

➙ l + b + 1 = 27

➙ l + b = 26 --------(2)

Adding equation (1) and (2),

➙ l + b + l - b = 30

➙ 2l = 30

➙ l = 15 m

Then,

➙ b = 26 - 15 = 11 m.

Hence:-

The original area of the floor will be$:$

= lb

= 15 × 11 m²

= 165 m²

Answer 2

$\Large\bf\blue{Let}$

• Breadth of a floor is x m.

Cᴀsᴇ - 1 ;-

• Length of a floor is 4 m more than it's breadth.

➙ Length of the floor = (x + 4) m

[NOTE :- Here the shape of the floor is rectangular.]

$\bf\pink{We\:know\:that,}$

$\red\bigstar\:\:{\underline{\green{\boxed{\bf{\color{peru}Area\:of\:the\:floor\:=\:Length\times{Breadth}\:}}}}}$

$\bf\purple{So,}$

$:\implies\:\:\bf{Area\:of\:the\:floor\:=\:(x\:+\:4)\times{x}\:}$

$:\implies\:\:\bf\orange{Area\:of\:the\:floor\:=\:(x^2\:+\:4x)\:m^2}$

Cᴀsᴇ - 2 ;-

• If both the length and breadth are
• increased by 1 m, then

➙ Length of the floor = (x + 4) + 1

➙ Length of the floor = (x + 5) m

$\bf\red{And,}$

➙ Breadth of the floor = (x + 1) m

$\bf\pink{Thus,}$

$:\implies\:\:\bf{Area\:of\:the\:floor\:=\:(x\:+\:5)\times{(x\:+\:1)}\:}$

$:\implies\:\:\bf{Area\:of\:the\:floor\:=\:x^2\:+\:5x\:+\:x\:+\:5\:}$

$:\implies\:\:\bf\green{Area\:of\:the\:floor\:=\:(x^2\:+\:6x\:+\:5)\:m^2}$

━─━─━─━─━─━─━─━─━─━─━─━─━─━─━

$\bf\blue{According\:to\:the\:question,}$

• After adding 1 m in both length & breadth, the area is increased by 27 m² from before.

=》(x² + 6x + 5) = (x² + 4x) + 27

=》(x² + 6x + 5) - (x² + 4x) = 27

=》x² + 6x + 5 - x² - 4x = 27

=》6x - 4x + 5 = 27

=》2x = 27 - 5

=》2x = 22

=》x = ²²/₂

=》x = 11

$\Large\bold\therefore$ The breadth of the floor is 11 m.

$\bf\purple{We\:have,}$

➙ Length of the floor = (x + 4) m

➙ Length of the floor = (11 + 4) m

➙ Length of the floor = 15 m

$\Large\bold\therefore$ The length of the floor is 15 m.

$\bf\orange{Again\:we\:have,}$

⇒ Area = Length × Breadth

⇒ Area = 15 × 11

⇒ Area = 165 m²

$\Large\bold\therefore$ The area of the floor is 165 m².