The width of the pool is 7 meters and the length is 15 meters.
Step-by-step explanation:
To find the length and width of the swimming pool, let's denote the width as "w" meters. According to the given information, the length is 8 meters longer than the width, so the length can be expressed as "w + 8" meters.
The formula to calculate the area of a rectangle is length multiplied by width. In this case, the area of the swimming pool is given as 105 square meters.
Area = Length * Width
105 = (w + 8) * w
Now, let's solve this equation to find the value of "w" (width).
Expanding the equation:
105 = w^2 + 8w
Rearranging the equation:
w^2 + 8w - 105 = 0
Now, we can solve this quadratic equation. Factoring or using the quadratic formula can help us find the values of "w" that satisfy this equation.
By factoring or using the quadratic formula, we find that the possible values for the width "w" are w = 7 or w = -15. Since a width cannot be negative, we discard the solution w = -15.
The width of the swimming pool is 7 meters.
To find the length, we can substitute this value of width back into the expression for length:
Answers & Comments
Answer:
The width of the pool is 7 meters and the length is 15 meters.
Step-by-step explanation:
To find the length and width of the swimming pool, let's denote the width as "w" meters. According to the given information, the length is 8 meters longer than the width, so the length can be expressed as "w + 8" meters.
The formula to calculate the area of a rectangle is length multiplied by width. In this case, the area of the swimming pool is given as 105 square meters.
Area = Length * Width
105 = (w + 8) * w
Now, let's solve this equation to find the value of "w" (width).
Expanding the equation:
105 = w^2 + 8w
Rearranging the equation:
w^2 + 8w - 105 = 0
Now, we can solve this quadratic equation. Factoring or using the quadratic formula can help us find the values of "w" that satisfy this equation.
By factoring or using the quadratic formula, we find that the possible values for the width "w" are w = 7 or w = -15. Since a width cannot be negative, we discard the solution w = -15.
The width of the swimming pool is 7 meters.
To find the length, we can substitute this value of width back into the expression for length:
Length = Width + 8 = 7 + 8 = 15 meters.