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, √20, 2√6 8, 15, 17 √7, √24, √25 35, 120, 125 21, 72, 78

Explanation:

Step1: Recall the property of similar triangles

Similar triangles have side - lengths in proportion. If the original side - lengths are \(a = 7\), \(b = 24\), \(c = 25\), for a set of side - lengths \(A\), \(B\), \(C\) to be similar, \(\frac{A}{7}=\frac{B}{24}=\frac{C}{25}=k\) (where \(k\) is a non - negative real number).

Step2: Check each option

• Option \(14,48,50\):

\(\frac{14}{7}=\frac{48}{24}=\frac{50}{25}=2\).

• Option \(9,12,15\):

\(\frac{9}{7}
eq\frac{12}{24}
eq\frac{15}{25}\).

• Option \(2,\sqrt{20},2\sqrt{6}\):

\(\frac{2}{7}
eq\frac{\sqrt{20}}{24}
eq\frac{2\sqrt{6}}{25}\).

• Option \(8,15,17\):

\(\frac{8}{7}
eq\frac{15}{24}
eq\frac{17}{25}\).

• Option \(\sqrt{7},\sqrt{24},\sqrt{25}\):

\(\frac{\sqrt{7}}{7}
eq\frac{\sqrt{24}}{24}
eq\frac{\sqrt{25}}{25}\).

• Option \(35,120,125\):

\(\frac{35}{7}=\frac{120}{24}=\frac{125}{25}=5\).

• Option \(21,72,78\):

\(\frac{21}{7}=\frac{72}{24}=\frac{78}{25}=3\).

Answer:

14, 48, 50; 35, 120, 125; 21, 72, 78