Observe the square below:
Determine the perimeter of the triangle ACD?
Observe the square below:
Determine the perimeter of the triangle ACD?
In order to answer the question, we first need to recall the properties of a square.
In a square, all the sides are equal. Therefore, the lengths of all sides, , , and are equal.
Since we denoted , we can state that:
Now let's remember another property of a square, which is that in a square all angles are equal to degrees.
This means that triangle is a right triangle, because angle C (which is part of the square) equals degrees.
In a right triangle, we can use another tool we have - the Pythagorean theorem.
The Pythagorean theorem allows us, in a right triangle, to determine the length of the third side using the other two sides as shown below:
C is the hypotenuse.
Therefore we can insert the given data:
Since we know that , the equation is as follows:
Thus we have found the third side of the triangle.
However we're not done yet!
Remember, we were asked to find the perimeter of triangle ACD,
Remember, the perimeter of a triangle is the sum of its sides.
That's the solution!