the length of a room is 5 feet less than twice the width if the length is nineteen feet what is the width
Answers
Answer:
The formula for the area of a rectangle is A = L * w. Substitute in your new expression for L. You should get
A = (2w - 5) * w.
You want an area that is less than 50 ft. So, A < 150.
Plug in your expression for A and solve for the inequality.
(2w - 5) * w < 150
2w2 - 5w < 150
2w2 - 5w - 150 < 0
2w2 - 5w - 150 = 0
(w - 10)(2w + 15) = 0 --> factor the expression
w - 10 = 0 2w + 15 = 0
w = 10 w = -15/2
Remember, the problem asks for the area of a rectangle. You can't have a negative width, so that eliminates answers involving w = -15/2.
Test values before and after w = 10
If w = 5
A = (2w - 5) * w = (2*5 - 5) * 5 = (10 - 5) * 5 = 5 * 5 = 25 < 150
If w = 20
A = (2w - 5) * w = (2*20 - 5) * 20 = (40 - 5) * 20 = 35 * 20 = 700 > 150
Thus, w < 10.
Alternatively, you can rationalize this by considering the relationship between the area and the width. The formula for the area of a rectangle is A = L * w. The area is directly proportional to the width, meaning that as the width increases, the area increases as well. Since you want the area to be less than 150, w cannot exceed 10.
The width is limited by the length, since the length cannot be less than zero. As a result, we get the inequality 2w - 5 > 0. When we solve this inequality, we get that w > 5/2.
Therefore, given the conditions in this problem, the 5/2 ft < w < 10 ft (don't forget units!) for the area of the rectangle to be less than 150 sq ft.
Step-by-step explanation:
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Answer:
Width of room =12 feet
Step-by-step explanation:
l=2b-5 ---(1)
if l=19 feet
Using equation (1)
19=2b-5
19+5=2b
24=2b
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or, b=12 feet