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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.

The numbers 7, 24, 25 form a Pythagorean triple. Which of these sets are the side-example-1
User Rysv
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1 Answer

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Since the numbers 7, 24, 25 form a Pythagorean triple

Then the similar triangle to this triangle must have multiple sides of 7, 24, 50 and make also Pythagorean triple

Let us check the answers

14, 48, 50


\begin{gathered} (14)/(7)=2 \\ (48)/(24)=2 \\ (50)/(25)=2 \end{gathered}

All sides have an equal ratio


\begin{gathered} 14^2+48^2=196+2304=2500 \\ 50^2=2500 \end{gathered}

They are a Pythagorean triple

Then 14, 48, 50 is similar to the given triangle

The first answer is correct

The 6th answer is 35, 120, 125


\begin{gathered} (35)/(7)=5 \\ (120)/(24)=5 \\ (125)/(25)=5 \end{gathered}

All sides have the same ratio


\begin{gathered} 35^2+120^2=1225+14400=15625 \\ 125^2=15625 \end{gathered}

Then 35, 120, 125 make Pythagorean triple

The 6th answer is correct

The answers are:

14, 48, 50 ------- 1st answer

35, 120, 125 ------ 6th answer

User Fafaro
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