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The length of a swimming pool is 8m longer than its width and the area is 105m^2 .
question.express the length and width form an equation and solve the misiing length and width

Sagot :

PlanetMech

Answer:

  • Express the length and width  in an equation:

for  W:  

W² + 8W - 105 = 0

for L:

L = 8m + W  

  • Solve the missing length and width

L = 15m

W = 7m

Solution:

Word Problem

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,  

  1. Express the length and width  in an equation.
  2. Solve the missing length and width

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:

Area of a rectangle = L × W

* 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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