Answer:
m = 3
Step-by-step explanation:
It is given that there are two triangles [tex]\triangle[/tex]ABC and
[tex]\triangle[/tex]ABC ~
Also, the sides are:
AB= 3
BC= 4
DE= 2m
EF= m+5 and
∠B≅∠E
Please have a look at the attached figure for [tex]\triangle[/tex]ABC and
The triangles are similar so as per the property of similar triangles, the ratio of corresponding sides will be same.
i.e.
[tex]\dfrac{AB}{DE} = \dfrac{BC}{EF}\\\Rightarrow \dfrac{3}{2m} = \dfrac{4}{m+5}\\\Rightarrow 3 \times (m+5) = 4 \times 2m\\\Rightarrow 3m +15= 8m \\\Rightarrow 5m=15\\\Rightarrow m = 3[/tex]
So, value of m = 3.
