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The length of a pool is 2 times its width plus 5, and the pool is surrounded by a deck which is 2 meters wide. If the total combined area is 741 square meters, find the dimensions of the pool.

Width: square meters
Length: square meter

User Yituo
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2 Answers

6 votes

Answer: width: 15 meters

length: 35 meter.

Explanation:

Let the length of a pool is x and the width of a pool is y.

Hence x=2y+5.

The length of a pool with a deck is x₁=2y+5+2+2 = 2y+9

The width of a pool with a deck is y₁=y+2+2=y+4

The total combined area is S₁=x₁*y₁=741 square meters.

So (2y+9)*(y+4)=741

2y²+8y+9y+36=741

2y² +17y-705=0

2y²-30y+47y-405=0

2y*(y-15)+47y*(x-15)=0

(y-15)*(2y+47)=0

y-15=0

y₁=15.

2y+47=0

2y=-47

Divide both parts of the equation by 2:

y=-23.5 ∉

Hence

x=2*15+5

x=30+5

x=35 meters

y=15 meters.

User TonyY
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The length of a pool is 2 times its width plus 5, and the pool is surrounded by a deck which is 2 meters wide. If the total combined area is 741 square meters, find the dimensions of the pool.

Width: square meters

Length: square meter

ChatGPT

Let's denote the width of the pool as 'w' (in meters).

According to the given information, the length of the pool is 2 times its width plus 5. Therefore, the length can be represented as (2w + 5) meters.

The pool is surrounded by a deck that is 2 meters wide on all sides. This means that both the width and length of the deck should be added to the dimensions of the pool to get the total combined area.

The total combined area is given as 741 square meters.

To calculate the dimensions of the pool, we need to subtract the area of the deck from the total combined area.

The area of the deck can be calculated as follows:

Area of the deck = 2 × (w + 2) + 2 × (2w + 5)

Now, we can calculate the area of the pool:

Area of the pool = Total combined area - Area of the deck

Area of the pool = 741 - (2 × (w + 2) + 2 × (2w + 5))

Simplifying the expression:

Area of the pool = 741 - (2w + 4 + 4w + 10)

Area of the pool = 741 - (6w + 14)

Area of the pool = 741 - 6w - 14

Area of the pool = 727 - 6w

Since we have the formula for the area of the pool, we can set it equal to the length multiplied by the width:

Area of the pool = Length × Width

727 - 6w = (2w + 5) × w

Now, let's solve this equation to find the value of 'w'.

727 - 6w = 2w² + 5w

2w² + 5w + 6w - 727 = 0

2w² + 11w - 727 = 0

We can solve this quadratic equation to find the value(s) of 'w'. By factoring or using the quadratic formula, we can determine the width of the pool.

User Daveraja
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