Question

$\pink{▬▬▬}$$\red{▬▬▬}$$\green{▬▬▬}$$\blue{▬▬▬}$$\orange{▬▬▬}$
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)​
$\pink{▬▬▬}$$\red{▬▬▬}$$\green{▬▬▬}$$\blue{▬▬▬}$$\orange{▬▬▬}$​

Answer 1

$\begin{gathered}\Large\bf\blue{Let} \\ \end{gathered}$

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.]

$\begin{gathered}\bf\pink{We\:know\:that,} \\ \end{gathered}$

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

$\begin{gathered}\bf\purple{So,} \\ \end{gathered}$

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

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

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

$\begin{gathered}\bf\red{And,} \\ \end{gathered}$

➙ Breadth of the floor = (x + 1) m

$\begin{gathered}\bf\pink{Thus,} \\ \end{gathered}$

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

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

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

$\pink{▬▬▬}$$\red{▬▬▬}$$\green{▬▬▬}$$\blue{▬▬▬}$$\orange{▬▬▬}$

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

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

$\huge&#8756$The breadth of the floor is 11 m.

$\begin{gathered}\bf\purple{We\:have,} \\ \end{gathered}$

➙ Length of the floor = (x + 4) m

➙ Length of the floor = (11 + 4) m

➙ Length of the floor = 15 m

$\huge&#8756$ The length of the floor is 15 m.

$\begin{gathered}\bf\orange{Again\:we\:have,} \\ \end{gathered}$

⇒ Area = Length × Breadth

⇒ Area = 15 × 11

⇒ Area = 165 m²

The area of the floor is 165 m²