# Thread: 4 more math questions

1. ## 4 more math questions

in attachments

think 17 is A. 25.6 not sure

2. Originally Posted by dgenerationx2
in attachments

think 17 is A. 25.6 not sure
you are correct (you used Pythagoras' Theorem, i suppose)

for 23 and 27 recall that the diagonals of a rectangle bisect each other (cut each other at their midpoints)

hint for 29, note that the diagonals are the same length, so AC = BD

3. Originally Posted by dgenerationx2
in attachments

think 17 is A. 25.6 not sure
17)
$\displaystyle \overline{NL} = 2\times\overline{JL} = 2\times 12.8 = 25.6$

OR

$\displaystyle \overline{NL} = \overline{MK}$

$\displaystyle \overline{MK} = \sqrt{\overline{NM}^2 + \overline{NK}^2} = \sqrt{16^2 +20^2} = \sqrt 656 \doteq 25.6$

23) and 27)
$\displaystyle \overline {RT} = \overline {TP} = \overline {PS}$

$\displaystyle \sqrt{(\overline {RT}+ \overline {TP})^2 - \overline {PS}^2} = \overline {SR}$

$\displaystyle \sqrt{(2\times\overline{RT})^2 - \overline{PS}^2} = \overline{SR}$

$\displaystyle \sqrt{(2\times5)^2 - 5^2} = \overline {SR}$

$\displaystyle \overline {SR} = \sqrt {75} = 5\sqrt{3} \doteq 8.7$

29)
$\displaystyle \overline{AC} = 3x$

$\displaystyle \overline{BD} = 7x - 8$

$\displaystyle \overline{AC} = \overline {BD}$

$\displaystyle 3x = 7x - 8$

$\displaystyle 4x = 8$

$\displaystyle x = 2$

$\displaystyle \overline{AC} = \overline {BD} = 3x = 3\times2 = 6$