two triangles are similar. the sides in order of smallest to largest of the smaller triangle are 3.5, y, and x. the sides in order of smallest to largest of the larger triangle are 7, x+4, and 3y. what are the values of the variable. (ps I took this from a picture so it makes more sense if u draw it)

Question

12-02-2015
Mathematics

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two triangles are similar. the sides in order of smallest to largest of the smaller triangle are 3.5, y, and x. the sides in order of smallest to largest of the larger triangle are 7, x+4, and 3y. what are the values of the variable. (ps I took this from a picture so it makes more sense if u draw it)

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AL2006 AL2006 · Answer 1 · 2015-02-12T19:20:46-05:00

Since the triangles are similar, the ratio of each side in one triangle to
the corresponding side in the other one is always the same number.
We know what one pair of sides is ... 3.5 and 7 ... so we know that
each side in the first triangle is 1/2 as long as the corresponding side
in the other one.

So we can say with assurance that ...

y = 1/2 (x + 4)
and
      x = 1/2 (3y) .

That's all the intelligence required for this problem. The rest is just algebra,
and I should not need to go through all the routine misery for you here.

When you solve this pair of equations slowly, carefully, and accurately,
you'll find that the sides of the triangles are ...

   3.5,   8, 12
and
   7, 16, 24 .