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Find x and the measures of the unknown sides of each triangle.

Find x and the measures of the unknown sides of each triangle.-example-1

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Answer:

  • x = 12
  • RS = RT = 31

Explanation:

You want the value of x and the measures of sides RS and RT in the isosceles triangle with RS = 3x -5 and RT = 2x +7, both marked with a single hash mark.

Congruence

Sides RS and RT are marked as congruent, so we have ...

RS = RT

3x -5 = 2x +7

x = 12 . . . . . . . . . add 5-2x

Then the side lengths are ...

RS = 3(12) -5 = 31

The value of x is 12, and the missing side lengths are RS=RT=31.

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