Jim has put a fence along the side AC of the triangular patch of land shown below.
A right angle triangle ABC is shown having length of one leg equal to 6 meters. The measure of angle ABC is 90 degrees. A fence is shown on the hypotenuse of the triangle. The length of the fence is 10m, the same as that of the hypotenuse.
What is the length of side AB?
Just recognize that this is a scaled-up 3-4-5 triangle.
To find the length of side AB, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we know the lengths of the two sides AC and BC. AC has a length of 6 meters and BC is the hypotenuse with a length of 10 meters.
Let's label the length of AB as x. We can set up the equation using the Pythagorean theorem:
x^2 + 6^2 = 10^2
Simplifying the equation, we have:
x^2 + 36 = 100
Subtracting 36 from both sides, we get:
x^2 = 64
Taking the square root of both sides, we have:
x = 8
Therefore, the length of side AB is 8 meters.