help asap please

Question

find the perimeter of the figure:

(triangle image to solve image link) :

https://drive.google.com/file/d/1uKuJI84u81kJq-EWYU4GhDqApcE-QGvG/view?usp=sharing

Answer 1

This picture can be broken down into a triangle and a square.

First, the square:

1. Two sides of the square are already given as being a distance of 8 units. Because we are solving for a perimeter and the fourth side of the square is attached to the triangle, we only count the three exterior sides that contribute to the perimeter: 8+8+8=24 units.

Second, the triangle:

1. Because the square borders the triangle and each side of the square are 8 units, we know that the far side of the triangle that borders the square is also 8 units. From this, we can use a little bit of trigonometry to solve for the other two sides of the triangle that contribute to the overall perimeter of the drawing.
2. For the hypotenuse, 8/sin(30) will tell us the hypotenuse length is 16 units.
3. For the adjacent side, 8/tan(30) will tell us the adjacent length is 13.86 units.

Now that we have found all of the sides of both the square and the triangle, we can add up the sides that contribute to the perimeter.

Perimeters are only the exterior sides of an object, so we add the three exposed sides of the square and the two exposed of the triangle to arrive at our perimeter: 8+8+8+16+13.86=53.86 units.

Answer 2

In a 30-60-90 triangle the long leg is √3 times the short leg.

(8)(8) = 64 this is the square

(0.5)(8√3)(8) = 32√3 this is the trinagle