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.

Answer 1

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