The perimeters of similar triangles are in the same ratio as the corresponding sidesanswers: always, never, sometimss

Always

Step-by-step explanation:

Suppose you have triangle ABC with side lengths a, b, c. Suppose that is similar to triangle DEF with side lengths d, e, f.

Now, let k be the ratio of corresponding sides ...

  k = d/a

Because the same factor applies to all sides, we also have ...

  k = e/b = f/c

That is, if we multiply by the denominators of each of these fractions, we get ...

The perimeter of ΔABC is ...

   perimeter(ABC) = a + b + c

The perimeter of ΔDEF is ...

  perimeter(DEF) = d + e + f = a·k + b·k + c·k

  perimeter(DEF) = k(a + b + c) = k·perimeter(ABC)

  k = perimeter(DEF)/perimeter(ABC)

That is, the perimeters are in the same ratio as corresponding sides.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1