Q:

PLS HELP ASAP I WILL IVE BRAINLIST ANSWER!!!!!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: mc011-1.jpg Leon states that 21, 28, 35 is a Pythagorean triple because the lengths found in step 2 form a Pythagorean triple. Which explains whether or not Leon is correct? Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple. Yes, any set of lengths with a common factor is a Pythagorean triple. No, the lengths of Pythagorean triples cannot have any common factors. No, the given side lengths can form a Pythagorean triple even if the lengths found in step 2 do not.

Accepted Solution

A:
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.