anonymous
  • anonymous
Two similar right triangles have areas of 6 square inches and
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Directrix
  • Directrix
and ...?
anonymous
  • anonymous
150 square inches. The length of the hypotenuse of the smaller triangle is 5 inches. What is the sum of the lengths of the legs of the larger triangle?
Directrix
  • Directrix
The ratio of the corresponding area from small to large = 6/150 = 1/25. For similar triangles, the square of the scale factor is the ratio of corresponding linear parts of the 2 trianlges. So the scale factor is 1 to 5 or 1/5. and....

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Directrix
  • Directrix
1/5 = 5/h where h is the hypotenuse of the larger triangle. h = 25.
Directrix
  • Directrix
The perimeters are also in the ratio 1/5 -- same as scale factor.
Directrix
  • Directrix
What is the sum of the lengths of the legs of the larger triangle? If the sides of the larger triangle form a Pythagorean triple, then that triple is (9, 12, 15) which is a multiple of (3,45). 9+12+15 = 36 - 15 = 21 for sum of legs.

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