Answer:
Leon is correct. (Option 1)
Step-by-step explanation:
Given that Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.
Step 1: Find the greatest common factor of the given lengths: 7
Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5
Step 3: Verify that the lengths found in step 2 form a Pythagorean triple.
we have to explain whether or not Leon is correct.
As, 3,4,5 forms a Pythagorean triplet i.e satisfies the Pythagoras theorem
[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]
⇒ [tex]5^2=3^2+4^2[/tex]
Let a, b, c forms a Pythagorean triplet
[tex]a^2+b^2=c^2[/tex]
Multiplied by 4 on both sides
⇒ [tex]4a^2+4b^2=4c^2[/tex]
⇒ [tex]{2a}^2+{2b}^2={2c}^2[/tex]
Hence, we say 4a, 4b and 4c also forms a Pythagorean triplet.
∴ multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
Hence, Leon is correct.
Answer:
The first one is correct!!
"Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple."
Step-by-step explanation:
