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3 : 5, 4: 5

Step-by-step explanation:

Let the common multiplier of the given ratios be x.

Therefore, lengths of the legs of right triangle would be 3x and 4x

By Pythagoras Theorem:

The answer to your question is:   p = 13     q = 13

Step-by-step explanation:

Obtain 2 equations where the unknown quantities are p and q.

A ( 7, 6)

B (-1, -2)

Equation 1         6 = p + 7q - 2(7)²

                         6 = p + 7q - 98

                         p + 7q = 104                      (1)

Equation 2       -2 = p - q - 2(-1)²

                        -2 = p - q - 2

                        p - q = 2 - 2

                        p - q = 0                           (2)

                        p = q

                       p + 7p = 104

                       8p = 104

                       p = 104/8

                       p = 13

                       q = 13