On a test I was given 2 triangles. One triangle gave measurements of all three sides as 2, 4, and 5. The next triangle had sides given 4 and 8 and it asked what the third side should be if the triangles were perpendicular.
How would I solve this? Do I find the perimeter of each triangle?
2 * 2 = 4
4 * 2 = 8
5 * 2 = ?
To solve this problem, you don't necessarily need to find the perimeter of each triangle. Since the question mentions that the triangles are perpendicular, it means that they are right triangles. In a right triangle, one of the angles is 90 degrees.
Let's start with the first triangle, which has sides measuring 2, 4, and 5. We can use the Pythagorean theorem to determine if it's a right triangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is side 5, and the other two sides are 2 and 4. We can test if it's a right triangle by checking if 5^2 = 2^2 + 4^2.
5^2 = 25
2^2 + 4^2 = 4 + 16 = 20
Since 25 is equal to 20, the first triangle is indeed a right triangle.
Now, let's move on to the second triangle, which has sides measuring 4 and 8. The question asks us to find the length of the third side if the triangle is perpendicular. Since we know it's a right triangle, we can use the Pythagorean theorem again.
Let's assume that the third side is "x." In this case, we can use the Pythagorean theorem to set up the equation:
x^2 = 4^2 + 8^2
x^2 = 16 + 64
x^2 = 80
To find the value of "x," we can take the square root of both sides:
x = √80
Simplifying the square root of 80 gives us:
x ≈ 8.94
Therefore, if the second triangle is perpendicular, the length of the third side should be approximately 8.94.