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: 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.

Step-by-step explanation:

The missing options are:

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.

A Pythagorean triple is a group of three integers (a, b and c) that satisfies the next equation:

c² = a² + b²

Multiplying the three integers by the same positive integer, you would get another Pythagorean triple.

(kc)² = (ka)² + (kb)²

k²c² = k²a² + k²b²

k²c² = k²(a² + b²)

c² = a² + b²

The procedure followed by Leon is the opposite. He found the greatest common factor and divided the given lengths by the greatest common factor, obtaining the simplest Pythagorean triple, which is (3,4,5)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is