Question

Please answer the file question

Answer 1

Answer:

  x = 15

Step-by-step explanation:

Corresponding sides have the same ratio:

  UV/PR = TV/QR

  (x +6)/14 = (x -3)/8

  4(x +6) = 7(x -3) . . . . . . multiply by 56

  4x +24 = 7x -21 . . . . . . eliminate parentheses

  45 = 3x . . . . . . . . . . . add 21-4x

  15 = x . . . . . . . . . . . .divide by 3

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Alternate solution

The long-side : short-side ratios for the two triangles are ...

  14 : 8 = (x +6) : (x -3)

If we look at the differences between the ratio numbers we see ...

  14 -8 = 6

  (x +6) -(x -3) = 9

That is, the numbers in the second ratio must be 9/6 = 3/2 times the numbers in the first ratio. In other words, ...

  x -3 = (3/2)(8) = 12

  x = 15

Check: x +6 = 3/2(14) ; 15 +6 = 21