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Triangle IJK is dilated by a scale factor of 3 to form triangle I^(')J^(')K '. Side J^(')K measures 75 . What is the measure of side JK ?

Triangle IJK is dilated by a scale factor of 33 to form triangle I′J′K \mathrm{I}^{\prime} \mathrm{J}^{\prime} \mathrm{K} '. Side J′K \mathrm{J}^{\prime} \mathrm{K} measures 7575 . What is the measure of side JK \mathrm{JK} ?

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Full solution

Q. Triangle IJK is dilated by a scale factor of 33 to form triangle I′J′K \mathrm{I}^{\prime} \mathrm{J}^{\prime} \mathrm{K} '. Side J′K \mathrm{J}^{\prime} \mathrm{K} measures 7575 . What is the measure of side JK \mathrm{JK} ?
  1. Triangle Dilation: Since the triangle IJKIJK is dilated by a scale factor of 33 to form triangle I′J′K′I'J'K', we know that each side of the new triangle is 33 times longer than the corresponding side of the original triangle.
  2. Side Length Calculation: To find the length of side JKJK, we divide the length of side J′K′J'K' by the scale factor.\newlineCalculation: 753=25\frac{75}{3} = 25.
  3. Final Result: So, the measure of side JKJK is 2525 units.

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