### Home > GC > Chapter 7 > Lesson 7.1.3 > Problem 7-31

7-31.

How long is the longest line segment that will fit inside a square of area

Draw a diagram. A square labeled, A, = 50.

Area of a square = *s*², where *s* = length of a side. Side labels added to square, on top & left sides, square root of 50.

Use the Pythagorean Theorem to solve for . Added to square, diagonal from, bottom left to top right, labeled, c.