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12 Oct 2020, 01:45
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (02:29) correct
36%
(02:17)
wrong
based on 39
sessions
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The diagonals of a convex quadrilateral, shown above, are perpendicular to each other. If three sides are equal to 3, 2, and 1, what is the length of the fourth side?
A. 2
B. \(\sqrt{6}\)
C. \(\sqrt{7}\)
D. 3
E. 4
Are You Up For the Challenge: 700 Level Questions
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12 Oct 2020, 02:29
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\(x1^2+x2^2=1 --- (1)\)
\(x2^2+x3^2=4 ---(2)\)
\(x3^2+x4^2=9 -- (3)\)
Subtracting equation 2 from 1
\(x3^2-x2^2=3 ---(4)\)
Subtracting 4 from 3
\(x4^2+x2^2=6\)
so \(\sqrt{6}\) is the answer, IMO
\(x2^2+x3^2=4 ---(2)\)
\(x3^2+x4^2=9 -- (3)\)
Subtracting equation 2 from 1
\(x3^2-x2^2=3 ---(4)\)
Subtracting 4 from 3
\(x4^2+x2^2=6\)
so \(\sqrt{6}\) is the answer, IMO
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06 Nov 2020, 03:20
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If a quadrilateral is orthodiagonal then the sum of squares of opposite sides equals each other:
1^2 + 3^3 = 2^2 + x^2
1 + 9 = 4 + x^2
x^2 = 6
x = sqrt(6)
1^2 + 3^3 = 2^2 + x^2
1 + 9 = 4 + x^2
x^2 = 6
x = sqrt(6)
