Answer:
[tex]BM = 14[/tex]
Step-by-step explanation:
Given
The attached triangles
Required
Find BM
We have that:
ABC is similar to JHG
This implies that:
AB corresponds to JH
BC corresponds to HG
AC corresponds to JG
BM corresponds to HN
Hence, HN can be solved using the following equivalent ratios
[tex]AB : BM = JH:HN[/tex]
From the attachment;
[tex]AB = 21; JH = 24[/tex]
So, we have:
[tex]21 : BM = 24:16[/tex]
Express as fraction
[tex]\frac{21 }{ BM }= \frac{24}{16}[/tex]
Cross multiply
[tex]BM * 24 = 21 * 16[/tex]
[tex]BM * 24 = 336[/tex]
Solve for BM
[tex]BM = 336/24[/tex]
[tex]BM = 14[/tex]
