The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and breadth of the pool?
VerifiedHint: Assume the breadth of the pool is x m. The length is 2 m more than twice its breadth. So, the length of the pool is (2x+2). The perimeter of the pool is 154 m. Now, put the values of the length, breadth and perimeter in the formula, \[Perimeter=2\left( length+breadth \right)\] . Now, get the value of x. The measure of breadth is x. Put the value of x in the equation (2x+2) and get the value of length. Now, we have the values of the length and the breadth.
Complete step by step solution:
According to the question, it is given that the perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth.
The perimeter of the rectangular swimming pool = 154 m ……………………………(1)
Let us assume the breadth of the perimeter be x.
The breadth of the rectangular swimming pool = x ………………………(2)
Since the length of the rectangular pool is 2 more than twice its breadth so, we get length as,
The length of the rectangular pool = 2x+2 ………………………(3)
Since the swimming pool is in the shape of a rectangle, here we can apply the formula of the perimeter of the rectangle.
We know the formula of the perimeter of the rectangle, \[Perimeter=2\left( length+breadth \right)\] ……………………………(4)
Now, putting the values of the breadth from equation (2) and length from equation (3), in equation (4), we get
\[\Rightarrow Perimeter=2\left( 2x+2+x \right)\]
\[\Rightarrow Perimeter=2\left( 3x+2 \right)\] ……………………………..(5)
From equation (1), we have the value of the perimeter.
Now, from equation (1) and equation (5), we get
\[ \Rightarrow 154=2\left( 3x+2 \right) \]
\[ \Rightarrow 77=3x+2 \]
\[ \Rightarrow 77-2=3x \]
\[ \Rightarrow 75=3x \]
\[ \Rightarrow \dfrac{75}{3}=x \]
\[ \Rightarrow 25=x \]
Now putting the value of x in equation (2) and equation (3), we get
The breadth of the rectangular swimming pool = 25 m.
The length of the rectangular pool = \[\left( 2\times 25+2 \right)=50+2=52\] m.
Therefore, the length and breadth of the rectangular swimming pool is 52 m and 25 m respectively.
Note: We can also solve this question without the use of the formula.
Let us assume the breadth of the perimeter be x.
The breadth of the rectangular swimming pool = x ………………………(1)
Since the length of the rectangular pool is 2 more than twice its breadth so, length is,
The length of the rectangular pool = 2x+2 ………………………(2)
We know that the perimeter of a rectangle is the summation of its all sides.
From equation (1) and equation (2)
We know that the opposite sides of a rectangle are equal.
So, Length=AB=CD=(2x+2) and Breadth=BC=AD=x.
Perimeter = Summation of all sides = AB+BC+CD+DA = 2x+2+x+2x+2+x=(6x+4) ……………………..(3)
It is given that the perimeter of the rectangular swimming pool = 154 m ………………………(4)
From equation (3) and equation (4), we get
\[ \Rightarrow 6x+4=154 \]
\[ \Rightarrow 6x=154-4 \]
\[ \Rightarrow 6x=150 \]
\[ \Rightarrow x=\dfrac{150}{6} \]
\[ \Rightarrow 25=x \]
Now putting the value of x in equation (1) and equation (2), we get
The breadth of the rectangular swimming pool = 25 m.
The length of the rectangular pool = \[\left( 2\times 25+2 \right)=50+2=52\] m.
Therefore, the length and breadth of the rectangular swimming pool is 52 m and 25 m respectively.
