5. Given the point T in rectangle ABCD, the distances from T to A,B,C is 15,20,25. Find the distance from T to D.
Problem
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Tags: geometry, rectangle
Mathnerd1223334444
21.06.2017 23:15
British Flag Theorem
equinox145111
21.06.2017 23:16
Oh that sounds like a fun theorem... What is it?
Mathnerd1223334444
21.06.2017 23:20
It says that $AT^2+CT^2=BT^2+DT^2$, meaning that $225+625=400+DT^2$, so $DT=\sqrt{450}=\boxed{15\sqrt{2}}$.
Mathster360
22.06.2017 06:26
equinox145111 wrote: Oh that sounds like a fun theorem... What is it? https://artofproblemsolving.com/wiki/index.php?title=Category:Theorems See here to learn more about theorems found in problem solving.
Rijadinho
26.04.2023 21:43
$AT^2+CT^2=BT^2+DT^2 \Rightarrow 15^2+25^2=20^2+DT^2$ $225+625=400+DT^2 \Rightarrow DT^2=450 \Rightarrow DT= \sqrt{450}$ $\blacksquare$