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In triangle PQR shown, triangles RPY and RYQ have areas 90 and 45 resp
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02 Feb 2022, 08:15
02 Feb 2022, 08:15
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85% (02:30) correct
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In triangle PQR shown, triangles RPY and RYQ have areas 90 and 45 respectively. If PY = XQ = 10, what is the length of \(\overline{XY}\)?
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Re: In triangle PQR shown, triangles RPY and RYQ have areas 90 and 45 resp
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24 Feb 2022, 23:28
24 Feb 2022, 23:28
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Carcass wrote:
Attachment:
GRE In triangle PQR shown, triangles.jpg
In triangle PQR shown, triangles RPY and RYQ have areas 90 and 45 respectively. If PY = XQ = 10, what is the length of \(\overline{XY}\)?
Show: ::
5
Let,
PX = a
XY = b
YQ = c, and
RQ = H
Area of triangles RPY = \(\frac{1}{2}(a+b)H = 90\)
Area of triangles RYQ = \(\frac{1}{2}(c)H = 45\)
Now, PY = XQ = 10
i.e. a + b = 10 = b + c
Area of triangles RPY = \(\frac{1}{2}(a+b)H = \frac{1}{2}(10)H = 90\)
\(H = 18\)
Area of triangles RYQ = \(\frac{1}{2}(c)H = \frac{1}{2}(c)(18) = 45\)
c = 5
Since, b + c = 10
b = 5 = XY
Re: In triangle PQR shown, triangles RPY and RYQ have areas 90 and 45 resp
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05 Oct 2024, 18:48
05 Oct 2024, 18:48
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