Question

1
3.
42. The breadth of a rectangular plot is
of its length. If the perimeter of
the plot is 240 meters. What is the
length of the plot?
(A) 80 m. (B) 240 m.
(C) 90 m. (D) None​

Answer 1

Correct Question:

• The breadth of a rectangular plot is one third of its length. If the perimeter of the plot is 240 meters. What is the length of the plot?

Answer :

• Length of the plot is 90m
• Option (c)

Given :

• The breadth of a rectangular plot is one third of its length
• Perimeter of the plot is 240m

To find :

• Length of the plot

Solution :

• Let the length of plot be x
• Breadth = 1/3 x

As we know that,

• Perimeter of rectangle = 2(length + breadth)

⟿ 2(length + breadth) = 240

⟿ 2(x + 1/3x) = 240

⟿ 2x + 2x/3 = 240

⟿ 6x + 2x / 3 = 240

⟿ 8x/3 = 240

⟿ 8x = 240 × 3

⟿ 8x = 720

⟿ x = 720/8

⟿ x = 90

Hence , Length of plot is 90m

• Breadth = 1/3x = 1/3 × 90 = 30m

So,

• Length of the plot is 90m
• Breadth of the plot is 30m

Verification :

As we know that,

• Perimeter of rectangle = 2(length + breadth)

⟿ 2(90 + 30)

⟿ 2(120)

⟿ 240

Answer 2

Correct Question :-

• The breath of a rectangular plot is on third of it's length. If the perimeter of the plot is 240 metres. What is the length of the plot ?

Given :-

• The breadth of a rectangular plot is one third of its length.
• Perimeter of the plot is 240m.

To find :-

• Find the Length of the plot ?

★ $\large\underline{\frak{As~we~know~that,}}$

$\large\dag$ Formula Used :

• $\boxed{\bf{Perimeter~of~rectangle~=~2(length~+~breadth)}}$

Solution :-

• Let the length of plot be x
• Breadth = $\large{\sf{\frac{1}{3}}}$x

:$\implies$2(length + breadth) = 240

$~~~~~$:$\implies$2(x + $\large{\sf{\frac{1}{3}}}$x) = 240

$~~~~~~~~~~$:$\implies$2x + $\large{\sf{\frac{2x}{3}}}$= 240

$~~~~~~~~~~~~~~~$:$\implies$6x + $\large{\sf{\frac{2x}{3}}}$= 240

$~~~~~~~~~~~~~~~~~~~~$:$\implies$$\large{\sf{\frac{8x}{3}}}$= 240

$~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$${\sf{8x~=~240~×~3}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$${\sf{8x~=~720}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$$\large{\sf{x~= \frac{720}{8}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$${\cancel{\dfrac{720}{8}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\pink{\frak{x~=~90}}}}}$

$\therefore$ Hence,

• The Length of the plot is = $\large\underline{\rm{90~m}}$.

$\large\star$Breadth = $\large{\sf{\frac{1}{3x}}}$= $\large{\sf{\frac{1}{3x}}}$ × ${\sf{90}}$ = $\large\underline{\rm{30~m}}$

Now,

• Length of the pole is = $\large{\rm\underline{90~m}}$
• Breadth of the pole is = $\large{\rm\underline{30~m}}$

V E R I F I C A T I O N :

★ $\large\underline{\frak{As~we~know~that,}}$

• $\boxed{\bf{Perimeter~of~rectangle~=~2(length + breadth)}}$

$\large\dashrightarrow$2(90 + 30)

$~~~~~$$\large\dashrightarrow$2(120)

$~~~~~~~~~~$$\large\dashrightarrow$${\underline{\boxed{\pink{\frak{240}}}}}$★

$\large\dag$ Hence Verified !!