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The diagonals of rectangle ABCD intersect at point Z. DZ = x + 6 and AC = 5x + 3 find the length of AC

The diagonals of rectangle ABCD intersect at point Z. DZ = x + 6 and AC = 5x + 3 find the length of AC
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The diagonals of rectangle ABCD intersect at point Z. DZ = x + 6 and AC = 5x + 3 find the length of AC

The diagonals of rectangle ABCD intersect at point Z. DZ = x + 6 and AC = 5x + 3 find-example-1
User Mjsey
by
9.2k points

1 Answer

1 vote

AC=BD, therefore

AC=BZ+ZD


\begin{gathered} 5x+3=x+6+x+6 \\ 5x+3=2x+12 \\ 5x+3-2x=2x+12-2x \\ 3x+3=12 \\ 3x+3-3=12-3 \\ 3x=9 \\ (3x)/(3)=(9)/(3) \\ x=3 \end{gathered}

then


AC=5x+3=5(3)+3=15+3=18

answer: AC= 18

User Chuck Callebs
by
8.1k points
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