Video Transcript
Find 𝑥 in the right triangle
shown.
We’re told that this is a right
triangle. And we can also identify this from
the figure as one of the interior angles has been marked with a small square. We’ve been given the lengths of two
of the triangle’s sides. 𝐼𝐽 is 17 units and 𝐼𝐾 is 15
units. 𝑥 is the length of the third side
in the triangle. And it’s this that we’re asked to
calculate.
We can recall that whenever we know
the lengths of two sides of a right triangle, we can calculate the length of the
third side by applying the Pythagorean theorem. This states that in any right
triangle, the square of the hypotenuse is equal to the sum of the squares of the two
shorter sides. If we label the lengths of the two
shorter sides as 𝑎 and 𝑏 and the length of the hypotenuse as 𝑐, this can be
written as 𝑎 squared plus 𝑏 squared equals 𝑐 squared.
In our triangle, 𝑥 is one of the
shorter sides. So we can form the equation 𝑥
squared plus 15 squared equals 17 squared. We now want to solve this equation
to find the value of 𝑥. Evaluating the squares gives 𝑥
squared plus 225 equals 289. We can then isolate the 𝑥 squared
term by subtracting 225 from each side of the equation, to give 𝑥 squared equals
64. Finally, we take the square root of
both sides, giving 𝑥 equals the square root of 64, which is eight. We’re only interested in the
positive solution here as 𝑥 represents a length.
So we’ve found the value of 𝑥;
it’s eight. Interestingly, as all the side
lengths in this right triangle are integer values, this is an example of a
Pythagorean triple, that is, a right triangle in which all three side lengths are
integers. Being able to recognize Pythagorean
triples can speed up some problems like these.
