the length of a pool is 30 meters greater than the width. if the area is 1000 square meters, find the dimensions of the pool.
L = W + 30
L * W = 1000
Substitute W+30 for L in the second equation and solve for W. Put that value in the first equation to find L. Check by putting both values into the second equation.
To find the dimensions of the pool, we can set up an equation based on the information given.
Let's say the width of the pool is represented by "w" meters.
Since the length is 30 meters greater than the width, the length can be represented as "w + 30" meters.
We know that the area of a rectangle is given by the formula: area = length * width.
In this case, the area is 1000 square meters, so we can set up the following equation:
w * (w + 30) = 1000
Now, we can solve this quadratic equation to find the dimensions of the pool.
w^2 + 30w - 1000 = 0
To solve this equation, we can factor it or use the quadratic formula.
Using the quadratic formula: w = (-b ± √(b^2 - 4ac)) / (2a),
where a = 1, b = 30, and c = -1000, we get:
w = (-30 ± √(30^2 - 4 * 1 * -1000)) / (2 * 1)
Simplifying further, we have:
w = (-30 ± √(900 + 4000)) / 2
w = (-30 ± √4900) / 2
w = (-30 ± 70) / 2
So we have two possible values for the width:
w₁ = (-30 + 70) / 2 = 40 / 2 = 20 meters
w₂ = (-30 - 70) / 2 = -100 / 2 = -50 meters
However, the width cannot be negative, so we discard w₂ = -50 meters.
Now we can find the length by adding 30 to the width:
length = width + 30
length = 20 + 30 = 50 meters
Therefore, the dimensions of the pool are width = 20 meters and length = 50 meters.