Question

the numbers 7, 24, 25 form a pythagorean triple. which of these sets are the side lengths of triangles similar to a triangle whose side lengths measure 7, 24, 25? select all the correct answers. 14, 48, 50 9, 12, 15 2, \sqrt{20}, 2\sqrt{6} 8, 15, 17 \sqrt{7}, \sqrt{24}, \sqrt{25} 35, 120, 125 21, 72, 78

Explanation:

Step1: Check similarity by ratio

For a set of numbers to be similar to \(7,24,25\), the ratios of corresponding sides should be equal.
For \(14,48,50\):
\(\frac{14}{7} = 2\), \(\frac{48}{24}=2\), \(\frac{50}{25}=2\)

Step2: Check another set

For \(35,120,125\):
\(\frac{35}{7}=5\), \(\frac{120}{24} = 5\), \(\frac{125}{25}=5\)

Step3: Check \(21,72,78\)

\(\frac{21}{7}=3\), \(\frac{72}{24}=3\), \(\frac{78}{25}=3.12\) (incorrect)
For \(9,12,15\):
\(\frac{9}{7}\approx1.29\), \(\frac{12}{24}=0.5\) (ratios not equal)
For \(2,\sqrt{20},2\sqrt{6}\):
\(\frac{2}{7}\approx0.29\), \(\frac{\sqrt{20}}{24}\approx\frac{4.47}{24}\approx0.19\) (ratios not equal)
For \(8,15,17\):
\(\frac{8}{7}\approx1.14\), \(\frac{15}{24}=0.625\) (ratios not equal)
For \(\sqrt{7},\sqrt{24},\sqrt{25}\):
\(\frac{\sqrt{7}}{7}\approx\frac{2.65}{7}\approx0.38\), \(\frac{\sqrt{24}}{24}\approx\frac{4.9}{24}\approx0.20\) (ratios not equal)

Answer:

14, 48, 50; 35, 120, 125