Question

Find a radical expression for the total
perimeter of the shaded triangles.

Answer 1

The total perimeter of the shaded triangles is
`-√(2) + √(5) + 6`

To find a radical expression for the total perimeter of the shaded triangles, we can add up the lengths of the sides of each triangle.

The length of the bottom side of each triangle is 2, and the length of the top side is the hypotenuse of a right triangle with legs of length 2 and 1. The hypotenuse can be found using the Pythagorean Theorem:

`c^2 = a^2 + b^2\\c^2 = 2^2 + 1^2\\c^2 = 5\\c = √(5)`

Therefore, the total perimeter of the shaded triangles is

`2 + 2 + 2 - √(2) + √(5)`

Simplified radical expression:
`-√(2) + √(5) + 6`