Two sides of a right triangle have lengths of 2 centimeters and 7 centimeters. the third side is not the hypotenuse. how long is the third side?

Use the Pythagorean Theorem: a² + b² = c².
a and b are the leg lengths and c is the hypotenuse.

The hypotenuse is the longest side of the three, so you know the hypotenuse is 7 cm.

We'll make 2 cm = a, and the third side = b.
Plug these into the formula.

2² + b² = 7²
4 + b² = 49
b² = 45
Square root b and 45 to find the length of the third side.

√b = √45
b = 6.71

The third side is 6.71 centimeters.

See below.

Step-by-step explanation:

Triangle ABC is congruent to triangle DEF (Given)

Angle ACB is congruent to angle ECG. (Vertical angles theorem)

Angle CEG is congruent to angle DEF. (Vertical angles theorem)

Angle DEF is congruent to angle ABC. (Definition of congruent triangles)

Angle CEG is congruent to angle ABC. (Substitution property of equality).

Triangle ABC is similar to triangle GEC. (Angle angle similarity postulate- if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.)