Answer:
[tex]m=3\frac{1}{3}[/tex]
Step-by-step explanation:
Given,
△ART∼△EFG
And also given that EG = GF
We have to find the measure of 'm'.
Solution,
Since △ART∼△EFG
So according to the property of similarity, which states that;
"If two triangles are similar then the ratio of corresponding sides are equal".
[tex]\frac{AR}{EF}=\frac{TR}{GF}[/tex]
And EG = GF,
So we can say that;
[tex]\frac{AR}{EF}=\frac{TR}{EG}[/tex]
Now putting the given values, we get;
[tex]\frac{12}{5}=\frac{8}{m}[/tex]
On using cross multiplication method, we get;
[tex]12m=5\times8\\\\m=\frac{5\times8}{12}=\frac{10}{3}=3\frac{1}{3}[/tex]
Hence the value of 'm' is [tex]3\frac{1}{3}[/tex].
