Question

What is the missing side

Answer 1

$\text{Use the Pythagorean theorem}\\\\leg^2+leg^2=hypotenuse^2\\\\x^2+\left(\dfrac{4}{7}\right)^2=\left(\dfrac{5}{7}\right)^2\\\\x^2+\dfrac{16}{49}=\dfrac{25}{49}\ \ \ \ \ |-\dfrac{16}{49}\\\\x^2=\dfrac{9}{49}\to x=\sqrt\dfrac{9}{49}}\\\\x=\dfrac{\sqrt9}{\sqrt{49}}\\\\x=\dfrac{3}{7}$

Answer 2

The Pythagorean theorem applies to the sides of this right triangle.

... x² + (4/7)² = (5/7)²

... x² = 25/49 -16/49

... x = √(9/49)

... x = 3/7

The unknown side has length 3/7.

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You might recognize that this is a 3-4-5 right triangle with a scale factor of 1/7.