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masha68 [24]
3 years ago
12

A rectangular rug has an area of 84 square feet. If its length is 2 feet more than twice its​ width, find the dimensions of the

rug.
The length of the rug is __. ____. (options for second blank box are feet, square feet, or cubic feet.
Mathematics
1 answer:
weeeeeb [17]3 years ago
3 0

L=2W+2

W=(L-2)/2

A=LW, using W from above makes this

A=L(L-2)/2

2A=L^2-2L

L^2-2L-2A=0, given A=84

L^2-2L-168=0

(L-14)(L+12)=0, since L>0

L=14

The length of the rug is 14 ft

(W=(L-2)/2=6 ft)

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Triangles abc, dbe, and fbg are all symmetric about the y-axis. what are the coordinates of the centroid?
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The coordinates of the centroid of a triangle whose vertices (x1, y1), (x2, y2), and (x3, y3) are (\frac{x1+x2+x3}{3} , \frac{y1+y2+y3}{3})

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∴ The coordinates of the centroid of Δ ABC are (0, 5)

In Δ DBE

∵ D = (-15, 0), B = (0, 15), E = (15, 0)

∴ x1 = -15, x2 = 0, x3 = 15

∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-15+0+15}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ DBE are (0, 5)

In Δ FBG

∵ F = (-5, 0), B = (0, 15), G = (5, 0)

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∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-5+0+5}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ FBG are (0, 5)

∵ The three triangles are symmetric about the y-axis

→ That means they have the same centroid and it lies on the y-axis

∴ The coordinates of the centroid are (0, 5)

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