Answer:
2√10
Step-by-step explanation:
Draw a vertical line through the corner between the side of length 7 and the side of length 5. This line forms a right triangle with hypotenuse 7 and base (8 - 5), or 3.
The Pythagorean Theorem applies here.
(hypotenuse)² = (base)² + (vertical side)² and this becomes:
7² = 3² + (vertical side)²
Solving this for (vertical side)², we get (vertical side)² = 49 - 9 = 40.
Thus, (vertical side) = √40 = √4·√10 = 2√10 (answer)
