Ellis's backyard has a 6.256.256, point, 25 by 6.25\,\text{m}6.25m6, point, 25, start text, m, end text patio. She would like to build a 1.5\,\text{m}1.5m1, point, 5, start text, m, end text wide extension around 333 sides of the patio, as the figure shows. She will buy 0.250.250, point, 25 by 0.25\,\text{m}0.25m0, point, 25, start text, m, end text tiles that come 252525 to a package.
Answers
Ellis need to buy 18/21 Packages to build the extension
Step-by-step explanation:
how many packages does ellis need to buy to build the extension?
Ellis's backyard has a 6.25 m * 6.25 m patio
She would like to build a 1.5 m wide extension around 3 sides of the patio,
Total Area = 3 * 6.25 * 1.5
She will buy 0.25 m * 0.25 m text tiles that come 25 to a package.
Area of tiles in= 0.25 * 0.25 = 0.0625
Number of Tiles required = 3 * 6.25 * 1.5 / (0.0625)
= 450
Number of Packages required = 450/25
= 18
Another possible solution depending upon configuration on configuration
Area of extension = (6.25 + 2*1.5)(6.25 + 1.5) - 6.25*6.25
= 32.625
Number of Tiles required = 32.625/0.0625
= 522
Package required = 522/25
= 20.88
= 21 Packages required
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Answer:
21
Step-by-step explanation:
Let's break up the extension into rectangles so we can determine its area.
There are 333 rectangles that are 6.25\,\text{m}6.25m6, point, 25, start text, m, end text by 1.5\,\text{m}1.5m1, point, 5, start text, m, end text and 222 squares with a side length of 1.5\,\text{m}1.5m1, point, 5, start text, m, end text.
3\cdot6.25 \cdot 1.5 + 2 \cdot 1.5^2=32.6253⋅6.25⋅1.5+2⋅1.5
2
=32.6253, dot, 6, point, 25, dot, 1, point, 5, plus, 2, dot, 1, point, 5, squared, equals, 32, point, 625
To build the extension, Ellis needs 32.625\,\text{m}^232.625m
2
32, point, 625, start text, m, end text, squared of tile.
Hint #22 / 5
Each tile is 0.25\,\text{m}0.25m0, point, 25, start text, m, end text wide and 0.25\,\text{m}0.25m0, point, 25, start text, m, end text long. So Ellis needs 161616 tiles to build 1\,\text{m}^21m
2
1, start text, m, end text, squared of the extension.
Hint #33 / 5
We can multiply the total area by the number of tiles to cover a square meter to find the total number of tiles Ellis needs.
32.625\,\cancel{\text{m}^2} \cdot 16\,\dfrac{\text{tiles}}{\cancel{\text{m}^2}}=522\,\text{tiles}32.625
m
2
⋅16
m
2
tiles
=522tiles32, point, 625, start cancel, start text, m, end text, squared, end cancel, dot, 16, start fraction, start text, t, i, l, e, s, end text, divided by, start cancel, start text, m, end text, squared, end cancel, end fraction, equals, 522, start text, t, i, l, e, s, end text
Hint #44 / 5
Ellis buys the tiles in packages of 252525 tiles per package.
\dfrac{522}{25}=20.88
25
522
=20.88start fraction, 522, divided by, 25, end fraction, equals, 20, point, 88
Since Ellis cannot buy part of a package, she will need 212121 packages to have enough tiles.
Hint #55 / 5
Ellis needs to buy 212121 packages of tiles to build the extension.