Question

) The perimeter of a rectangular swimming pool is 154

meters. Its length is 2m more than twice its breadth. What

are the length and the breadth of the pool​

Answer 1

Answer:

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?

Answer Verified Verified

Hint: 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(length+breadth)Perimeter=2(length+breadth) . 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(length+breadth)Perimeter=2(length+breadth) ……………………………(4)

Now, putting the values of the breadth from equation (2) and length from equation (3), in equation (4), we get

⇒Perimeter=2(2x+2+x)⇒Perimeter=2(2x+2+x)

⇒Perimeter=2(3x+2)⇒Perimeter=2(3x+2) ……………………………..(5)

From equation (1), we have the value of the perimeter.

Now, from equation (1) and equation (5), we get

⇒154=2(3x+2)⇒77=3x+2⇒77−2=3x⇒75=3x⇒753=x⇒25=x⇒154=2(3x+2)⇒77=3x+2⇒77−2=3x⇒75=3x⇒753=x⇒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 = (2×25+2)=50+2=52(2×25+2)=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

⇒6x+4=154⇒6x=154−4⇒6x=150⇒x=1506⇒25=x⇒6x+4=154⇒6x=154−4⇒6x=150⇒x=1506⇒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 = (2×25+2)=50+2=52(2×25+2)=50+2=52 m.

Therefore, the length and breadth of the rectangular swimming pool is 52 m and 25 m respectively.

Answer 2

Answer:

length = 52m

breadth = 25m

Step-by-step explanation:

Here, b=b

And, l=2b+2

Perimeter of a rectangle = 2(l+b) = 2(2b+2+b) = 6b+4 = 154(given)

=>b = 25

=>2b+2 = l = 52