Question

Solution
Rati
2. The length of a rectangular swimming
pool is 5 m more than two times its
breadth. Find the length and breadth
of the pool if its perimeter is 160 m.

​

Answer 1

Given:-

• Perimeter of pool = 160 m

• length of a rectangular swimming pool is 5 m more than two times its breadth

To find:-

• Length of swimming pool

• Breadth of swimming pool

Let:-

• Breadth of swimming pool be x

• Length of swimming pool be 5 + 2x

Solution:-

We know:

$\bigstar \boxed{ \rm{}Perimeter \: of \: rectangle = 2(length + breadth)}$

By using this formula we can find value of Perimeter of rectangle

$\dashrightarrow \: \sf{}Perimeter \: of \: rectangle = 2(length + breadth)$

$\dashrightarrow \: \sf{}160= 2( \{5 + 2x \} + \{x \})$

$\dashrightarrow \: \sf{}160= 2\{5 + 2x \} + 2 \{x \}$

$\dashrightarrow \: \sf{}160= 2\{5 + 2x \} + 2 x$

$\dashrightarrow \: \sf{}160= \{2 \times 5 + 2 \times 2 \}+ 2 x$

$\dashrightarrow \: \sf{}160= \{10 + 4x \}+ 2 x$

$\dashrightarrow \: \sf{}160= 10 + 4x + 2 x$

$\dashrightarrow \: \sf{}160= 10 +6x$

$\dashrightarrow \: \sf{}10 +6x = 160$

$\dashrightarrow \: \sf{}6x = 160 - 10$

$\dashrightarrow \: \sf{}6x = 150$

$\dashrightarrow \: \sf{}x = \frac{150}{6}$

$\dashrightarrow \: \sf{}x = \frac{25 \times 6}{6}$

$\dashrightarrow \: \sf{}x = \frac{25 \times \cancel6}{ \cancel6}$

$\dashrightarrow \: \sf{}x = 25 \times 1$

$\dashrightarrow \: \sf{}x = \textsf{ \textbf{25 }}$

Now Let's Verify value of x:-

$\dashrightarrow \: \sf{}160= 2( \{5 + 2 \times 25 \} + \{25\})$

$\dashrightarrow \: \sf{}160= 2( \{5 + 2 \times 25 \} +25)$

$\dashrightarrow \: \sf{}160= 2( \{5 +50 \} +25)$

$\dashrightarrow \: \sf{}160= 2( \{55\} +25)$

$\dashrightarrow \: \sf{}160= 2( 55 +25)$

$\dashrightarrow \: \sf{}160= 2(80)$

$\dashrightarrow \: \textsf{ \textbf{160= 160}}$

LHS = RHS

Hence verified!

Finally:-

To find breadth of swimming pool:-

$\textsf{Breadth of swimming pool = x}$

$\leadsto \textsf{Breadth of swimming pool = \textbf{ 25 m}}$

To find Length of swimming pool:-

$\textsf{Length of swimming pool = 5 + 2x}$

$\leadsto\textsf{Length of swimming pool = 5 + 2 \times 25}$

$\leadsto\textsf{Length of swimming pool = 5 +50}$

$\leadsto\textsf{Length of swimming pool = \textbf{55 \: m}}$

Answer 2

Given :-

• The length of a rectangular swimming pool is 5 m more than two times its breadth
• Perimeter of Pool = 160m

To Find :-

• Length and Breadth of Pool

Solution :-

⟾ Let the Breadth of Pool be x

⟾ Then Length of Pool will be 5 + 2x

According to the Question :

➞ Perimeter of Rectangle = 2 ( L + B )

➞ 160 = 2 ( 5 + 2x + x )

➞ 160 / 2 = 5 + 2x + x

➞ 80 = 5 + 3x

➞ 80 - 5 = 3x

➞ 75 = 3x

➞ 75 / 3 = x

➞ 25 = x

________________

Verification :

➞ Perimeter of Pool = 2 ( L + B )

➞ Perimeter of Pool = 2 ( 5 + 2x + x )

➞ Perimeter of Pool = 2 ( 5 + 3x )

➞ Perimeter of Pool = 2 ( 5 + 3 × 25)

➞ Perimeter of Pool = 2 ( 5 + 75 )

➞ Perimeter of Pool = 2 × 80

➞ 160 = 160

Hence Verified

________________

Therefore :

• Length = 5 + 2x = 5 + 2 × 25 = 5 + 50 = 55m
• Breadth = x = 25m

________________

★ Additional Info :

Formulas Related to Rectangle:

• Perimeter of Rectangle = 2( l + b)
• Area = Length × Breadth
• Length = Area / Breadth
• Breadth = Area / Length
• Diagonal = √(l)² + (b)²

________________