The lengths of the sides of a triangle are 3,4, and 6. If the length of the shortest side of a similar triangle is 5, find the length of its longest side.

The illustration of this scenario is shown in the attached photo. The small triangle is triangle ABC and it corresponds to a bigger triangle XYZ. This also means that triangle ABC is similar to triangle XYZ. This means that the ratio of a side on the small triangle to a corresponding side on the bigger triangle is constant or proportional. Therefore,

AB/XY = AC/XZ = BC/YZ

We want to find the length of the longest side of the bigger triangle. Let x = the length of the longest side of the bigger triangle. It becomes

BC/YZ = AC/XZ

6/x = 3/5

3x = 30

x = 30/3 = 10

Branta Branta · Answer 2 · 2019-11-20T08:32:13+01:00

Answer:

10

Step-by-step explanation:

Sides of the given triangle are 3,4,6

Corresponding shortest side of the similar triangle is 5.

As per law of similar triangles, ratio of corresponding sides of two similar triangles is equal. Hence, \[(shortest1/longest1) = (shortest2/longest2)\]

Substituting the relevant values:

\[3/6 = 5/longest2\]

=> \[longest2 = 5*6/3\]

=> \[longest2 = 30/3 = 10\]

Hence the length of the longest side of the similar triangle is 10.