Answer:
for W:
W² + 8W - 105 = 0
for L:
L = 8m + W
L = 15m
W = 7m
Solution:
In order for us to find out the equation that will help us solve the missing length and width, let's first list down the given.
Given:
W = ? (width of the swimming pool)
L = ? (length of the swimming pool)
hint : length is 8m longer than the width
A = 105 m²
Required:
There are two required from this problem,
Solution:
In order to find out the area of the rectangular* swimming pool, we need to know first the standard equation for finding the area of a rectangle:
* Although it is not given that it is a rectangle, the problem itself gave us a hint that the sides of the pool are not equal. Thus satisfies the property of a rectangle where 2 sides are equal.
Let's now proceed in solving the problem.
Since length is 8m longer than the width, thus,
L = 8m + W → eq. 1
Since
A = 105 m²
thus,
105 m² = L × W → eq. 2
Let's express equation 2 in terms of W.
105 m² = (8m + W) × W
105 m² = (8W)m + W²
Simplifying - (lets set aside the m unit) an turn the equation to a quadratic standard form.
W² + 8W - 105 = 0
Thus,
(W - 7) ; (W + 15)
This will give us 2 values for W but we will only choose the value that would satisfy the given equations. Since the other factor is a negative, we will choose the positive integer as a negative integer would give us non-existent values.
W = 7 → eq. 3
W = -15
Thus,
L = 8 + 7
L = 15 → eq. 4
Substituting the values to equation 2 for checking
105 m² = 15m × 7m
105 m² = 105 m²
Therefore;
L = 15m
W = 7m
For solving word problems you may check the below link:
https://brainly.ph/question/2275962
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