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x or y
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24 Sep 2018, 12:01
24 Sep 2018, 12:01
Expert Reply
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Question Stats:
53% (01:49) correct
46% (02:08) wrong based on 65 sessions
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\(\overline{AD} =2\)
\(\overline{DC}=x\)
\(\overline{CE}=8\)
\(\overline{BE}=y\)
\(\overline{DE}\) is parallel to \(\overline{AB}\)
Quantity A |
Quantity B |
x |
y |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: x or y
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08 Nov 2018, 21:48
08 Nov 2018, 21:48
1
Expert Reply
Carcass wrote:
Attachment:
triangle.jpg
\(\overline{AD} =2\)
\(\overline{DC}=x\)
\(\overline{CE}=8\)
\(\overline{BE}=y\)
\(\overline{DE}\) is parallel to \(\overline{AB}\)
Quantity A |
Quantity B |
x |
y |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Hi..
since \(\overline{DE}\) is parallel to \(\overline{AB}\), triangle ABC and CDE are similar triangles. This means the sides are in proportion..
ABC similar DEC .. thus
\(\frac{AB}{DE}=\frac{BC}{EC}=\frac{CA}{CD}.............\frac{15}{10}=\frac{8+y}{8}=\frac{x+2}{x}\)..
\(\frac{15}{10}=\frac{8+y}{8}........15*8=10*(8+y)......y=\frac{8*(15-10)}{10}=4\)
\(\frac{15}{10}=\frac{x+2}{x}........15*x=10*(x+2)......x=\frac{20}{(15-10)}=4\)
so x=y
C
