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son4ous [18]
3 years ago
5

If triangle ABC is similar to triangle PQR, find the value of x and y.

Mathematics
1 answer:
tester [92]3 years ago
6 0

Answer:

x = 9

y = 6

Step-by-step explanation:

ΔABC ~ ΔPQR

Therefore, corresponding sides of these similar triangles will be in the proportional.

\frac{AB}{PQ}=\frac{BC}{QR}= \frac{AC}{PR}

\frac{6}{x}= \frac{4}{y}= \frac{8}{12}

\frac{6}{x}= \frac{8}{12}

x = \frac{12\times 6}{8}

x = 9

Similarly, \frac{4}{y}= \frac{8}{12}

y = \frac{12\times 4}{8}

y = 6

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3 years ago
an athletic facility is building an indoor track. the track is composed of a rectangle and two semicircles, as shown. a) write a
stepan [7]

Answer:

(a) P = 2x + 2r + 2πr

(b) x = ½(P - 2r - 2πr)

(c) x = 123 feet

Step-by-step explanation:

See Attachment for sketch of the track

Solving for (a): Perimeter of the track

This is calculated by adding the perimeter of the rectangle to the 2 semicircles as follows.

P = Perimeter of Rectangle + Perimeter of 2 Semicircles

P = 2(x + r) + 2 * πr

[Where r is the radius of both semicircles]

Open bracket

P = 2x + 2r + 2πr

Solving for (b): Formula for x

P = 2x + 2r + 2πr

Make x the subject of formula

2x = P - 2r - 2πr

Divide both sides by 2

x = ½(P - 2r - 2πr)

Solving for (c): the value of x when r = 50 and P = 660

Substitute the given values in the formula in (b) above

x = ½(P - 2r - 2πr)

x = ½(660 - 2 * 50 - 2π * 50)

x = ½(660 - 100 - 100π)

x = ½(560 - 100π)

Take π as 3.14

x = ½(560 - 100 * 3.14)

x = ½(560 - 314)

x = ½ * 246

x = 123 feet

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3 years ago
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(I'm having trouble attaching the graphic - I think the problem is with Brainly).

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3 0
3 years ago
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alexandr1967 [171]
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8 0
3 years ago
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