the floor of a conference hall can be covered completely with tiles it its length is 36 feet longer than its width the area of the floor is less than 2040 square feet how would you represent the width of the floor how about its length
Answers
Given : length is 36 feet longer than its width the area of the floor is less than 2040 square feet
To Find : the width of the floor
and Length of Floor
Solution:
Let say Width of the Floor = W feet
length is 36 feet longer than its width
Length = W + 36 Feet
area of the floor is less than 2040 square feet
Area = Length x Width
= (W + 36) W
(W + 36) W < 2040
=> W² + 36W < 2040
=> W² + 36W + 18² < 2040 + 18²
=> (W + 18)² < 48.62
| W + 18 | < 48.62
=> -48.62 < W + 18 < 48.62
=> -66.62 < W < 30.62
Width can not be -Ve
Hence 0 < W < 30.62
Width is less than 30.62 feet
Length is less than 66.62 feet
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Explanation:
Given the floor of a conference hall can be covered completely with tiles it its length is 36 feet longer than its width the area of the floor is less than 2040 square feet how would you represent the width of the floor how about its length
- Let l be the length and w be the width of the floor.
- According to the question length is 36 feet longer than its width
- So l = 36 + w
- Also Area is less than 2040 sq ft
- So we have Area = length x width
- So 2040 = (36 + w) w
- So 36 w + w^2 = 2040
- Or w^2 + 36 w – 2040 = 0
- So we have w = - b +-√b^2 – 4ac / 2a
- = - 36 + - √36^2 – 4 (-2040) / 2(1)
- = - 36 + - √36^2 + 8160 / 2
- = - 36 + - √9456 / 2
- Or w = 30.62 ft
- Now l = 36 + w
- = 36 + 30.62
- l = 66.62
- Also Area = length x width
- = 66.2 x 30.62
- = 2039.90 sq ft
Reference link will be
https://brainly.ph/question/5815911