Respuesta :
Answer:
The width of the border will be 3/2 ft or 1.5 ft
Step-by-step explanation:
The rectangular swimming pool is 8 ft wide and 14 ft long. A tile border is built around the pool of uniform width. The tile border is 75 ft². The illustration below is just like a rectangle inside another rectangle.
The tile border around the pool has a uniform width. The width was added to both end of the length and the width of the rectangular pool.
Let
The added width = a
On both end the added width will be
(8 + 2a) and (14 + 2a)
The area of the whole rectangle formed including the border
(8 + 2a) (14 + 2a)
The area of the rectangular swimming pool
8 × 14 = 112 ft²
The area of the border(75 ft²)
(8 + 2a) (14 + 2a) - 112 = 75
112 + 16a + 28a + 4a² - 112 = 75
4a² + 44a - 75 = 0
find the numbers you multiply to get -75 × 4 = -300 and also add to get 44. The numbers are - 6 and 50.
4a² - 6a + 50a - 75 = 0
2a(2a - 3) + 25(2a - 3) = 0
(2a−3)(2a+25)
2a - 3 = 0 or 2a + 25 = 0
a = 3/2 or a = -25/2
we will use a = 3/2 since it is positive.
The width of the border will be 3/2 ft or 1.5 ft
Width of the tiles border around the rectangular pool will be 1.5 feet.
Area of a rectangle:
- Area of a rectangle is given by the expression,
Area = Length × Width
Given in the question,
- Dimensions of the pool → 14 feet by 8 feet
- Area of the border around the pool = 75 square feet
By using the expression for the area of a rectangle,
Area of rectangular pool = 14 ×8
= 112 square feet
Let the width of the border around the pool = x feet
Therefore, length of the border around the pool = (14 + 2x) feet
And width of the border around the pool = (8 + 2x) feet
Area of the border = Area of the border including pool - Area of the pool
75 = (14 + 2x)(8 + 2x) - 112
14(8 + 2x) + 2x(8 + 2x) = 75 + 112
112 + 28x + 16x + 4x² = 187
4x² + 44x + 112 = 187
4x² + 44x - 75 = 0
4x² + 50x - 6x - 75 = 0
2x(2x + 25) - 3(2x + 25) = 0
(2x - 3)(2x + 25) = 0
x = -12.5, 1.5
Therefore, width of the border will be 1.5 feet (Since, width can't be negative in measure).
Learn more about the area of the rectangular shapes here,
https://brainly.com/question/2292444?referrer=searchResults
