x is in meters.25. Dimensions of a Rug Zachary wants to buy a rug for a room that is 12 ft wide and15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford tobuy 108 ft2 of carpeting. What dimensions should the rug have?108 ft12 ftA15 ft-26. Width of a Flower Border A landscape architect has included a rectangular flowerbed measuring 9 ft by 5 ft in her plans for a new building. She wants to use twocolors of flowers in the bed: one in the center and the other for a border of the samewidth on all four sides. If she has enough plants to cover 24 ft2 for the border, howwide can the border be?27. Volume of a Box A rectangular piece of metal is 10 in. longer than it is wide.Squares with sides 2 in. longupward to form an open box. If the volume of the box is 832 in.3, what were theoriginal dimensions of the piece of metal?are cut from the four corners, and the flapsare folded28, Volume of a Box In Exercise 27, suppose that the piece of metal has length twicethe width, and 4-in. squares are cut from the corners. If the volume of the box is1536 in.3, what were the original dimensions of the piece of metal?

Question
Asked Aug 30, 2019

How do you answer question twenty-seven?

x is in meters.
25. Dimensions of a Rug Zachary wants to buy a rug for a room that is 12 ft wide and
15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford to
buy 108 ft2 of carpeting. What dimensions should the rug have?
108 ft
12 ft
A
15 ft-
26. Width of a Flower Border A landscape architect has included a rectangular flower
bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two
colors of flowers in the bed: one in the center and the other for a border of the same
width on all four sides. If she has enough plants to cover 24 ft2 for the border, how
wide can the border be?
27. Volume of a Box A rectangular piece of metal is 10 in. longer than it is wide.
Squares with sides 2 in. long
upward to form an open box. If the volume of the box is 832 in.3, what were the
original dimensions of the piece of metal?
are cut from the four corners, and the flaps
are folded
28, Volume of a Box In Exercise 27, suppose that the piece of metal has length twice
the width, and 4-in. squares are cut from the corners. If the volume of the box is
1536 in.3, what were the original dimensions of the piece of metal?
help_outline

Image Transcriptionclose

x is in meters. 25. Dimensions of a Rug Zachary wants to buy a rug for a room that is 12 ft wide and 15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford to buy 108 ft2 of carpeting. What dimensions should the rug have? 108 ft 12 ft A 15 ft- 26. Width of a Flower Border A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two colors of flowers in the bed: one in the center and the other for a border of the same width on all four sides. If she has enough plants to cover 24 ft2 for the border, how wide can the border be? 27. Volume of a Box A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. long upward to form an open box. If the volume of the box is 832 in.3, what were the original dimensions of the piece of metal? are cut from the four corners, and the flaps are folded 28, Volume of a Box In Exercise 27, suppose that the piece of metal has length twice the width, and 4-in. squares are cut from the corners. If the volume of the box is 1536 in.3, what were the original dimensions of the piece of metal?

fullscreen
check_circleExpert Solution
Step 1

Given rectangular piece has a square with sides 2-in.

So, consider it as the height of the box.

Consider l and w as the length and width of the rectangular metal piece.

Since the length of metal piece is 10-in longer than its width, l = w + 10.

Now draw a open box with denote the above information in it as shown in below figure.

w +6
2-in
w-4
l w10
help_outline

Image Transcriptionclose

w +6 2-in w-4 l w10

fullscreen
Step 2

First obtain the volume of box by the formu...

V length x width x height
X
832 (w10-4) x (w -4)x2
832
(w 6)(w-4)
2
w22w24= 416
w22w-24-416=0
+
w2w-440= 0
(w 22)(w-20)
w-22 or 20
Since, the width cannot be negative, here -22 for w can be eliminated
So, the width of box is 20-in.
help_outline

Image Transcriptionclose

V length x width x height X 832 (w10-4) x (w -4)x2 832 (w 6)(w-4) 2 w22w24= 416 w22w-24-416=0 + w2w-440= 0 (w 22)(w-20) w-22 or 20 Since, the width cannot be negative, here -22 for w can be eliminated So, the width of box is 20-in.

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

Math

Algebra

Other