1 Answer

Dercz · Answer 1 · 2023-09-01T01:53:39+0000

$\huge\begin{array}{ccc}BT=21\\DC=10.2\end{array}$

If BT is the midsegment of ΔMAH and DC is the midsegment of ΔBTH, then MA, BT and DC are parallel.

Therefore the segments form the proportion:

(HM)/(MA)=(HB)/(BT)=(HD)/(DC)

BT is the midsegment of ΔMAH, therefore

HB=(1)/(2)HM

DC is the midsegment of ΔBTH, therefore

$HD=(1)/(2)HB=(1)/(2)\cdot(1)/(2)HM=(1)/(4)HM$

(HM)/(42)=((1)/(2)HM)/(BT)

cross multiply

$HM\cdot BT=42\cdot(1)/(2)HM$

divide both sides by HM

$\boxed{BT=21}$

(HM)/(42)=((1)/(4)HM)/(DC)

cross multiply

$HM\cdot DC=42\cdot(1)/(4)HM$

divide both sides by HM

$\boxed{DC=10.5}$

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