Question

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topic: similar figures. question: find the sides marked with letters.All lengths are given in centimeters. please help me find 'n'​​

Answer 1

Answer:

$\sf n = 6$  and $\sf m= 6$

solving similarities

given: ΔBAC = ΔDBC

solve for m

$\sf \frac{BA}{BC} = \frac{DB}{DC}$

$\sf \frac{m}{4} = \frac{3}{2}$

$\sf m= \frac{4*3}{2}$

$\sf m= 6$

solve for n

$\sf \frac{BA}{AC} = \frac{DB}{BC}$

$\sf \frac{6}{n+2} = \frac{3}{4}$

$\sf 3(n+2) = 24$

$\sf (n+2) = 8$

$\sf n = 8-2$

$\sf n = 6$

Answer 2

In ∆ABD and ∆BCD

$\\ \rm\hookrightarrow \dfrac{m}{3}=\dfrac{4}{2}$

$\\ \rm\hookrightarrow m/3=2$

$\\ \rm\hookrightarrow m=3(2)$

$\\ \rm\hookrightarrow m=6$

In ∆ABC

$\\ \rm\hookrightarrow \dfrac{m}{4}=\dfrac{n}{2}$

$\\ \rm\hookrightarrow \dfrac{6}{4}=\dfrac{n}{2}$

$\\ \rm\hookrightarrow 3/2=n/2$

$\\ \rm\hookrightarrow n=6/2$

$\\ \rm\hookrightarrow n=3$