A Pythagorean Triple is a set of three nonzero whole numbers a, b, and c, that satisfy the equation a^2 +b^2=c^2.
Let's list some of the common Pythagorean Triples.
Common Pythagorean Triples
a^2+b^2=c^2
3, 4, 5
3^2+ 4^2= 5^2
5, 12, 13
5^2+ 12^2= 13^2
8, 15, 17
8^2+ 15^2= 17^2
7, 24, 25
7^2+ 24^2= 25^2
Here we want to use a Pythagorean Triple to find the value of x in the given triangle.
To find x, we can start by finding a common factor of the given values. Notice that 78 and 72 are both multiples of 6. This means that we can rewrite them as a product of 6 and other number. Let's do it!
6 * 13= 78
6 * 12= 72
Now, since 5, 12, 13 is a Pythagorean Triple, the missing length x must also fit this pattern. Therefore, the missing length will be a product of 5 and 6.
6 * 5 = 30
We can check this by substituting these values into the Pythagorean Theorem.
30^2+ 72^2 ? = 78^2
⇕
6084=6084 âś“
We end up with a true statement so our solution is correct.
