Question

Find the length of GL for square GLJK.

Answer 1

`2.5 √(2)`

Explanation:

Given:

A square GHJK

l (side length) = 5

Find: GL- ?

First, we can find the length of the diagonal GJ from ∆GJK by using the Pythagorean theorem:

`{gj}^(2) = {gk}^(2) + {jk}^(2)`

`{gj}^(2) = {5}^(2) + {5}^(2) = 25 + 25 = 50`

`gj > 0`

`gj = √(50) = √(25 * 2) = 5 √(2)`

The diagonals of the square bisect each other when they intersect, so GL will be equal to half the diagonal (intersection point L):

`gl = 0.5 * gj = 0.5 * 5 √(2) = 2.5 √(2)`