the perimeter of a rectangular swimming pool is 164 m. It's length is 2m more than Twince it's breath. What are the length and the breath of the pool?
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CBSE
Mathematics
Grade 9
Perimeter of a rectangle
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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?
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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)
. 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)
……………………………(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(3x+2)
……………………………..(5)
From equation (1), we have the value of the perimeter.