Before we begin, recall that a Pythagorean Triple is a set of three nonzero whole numbers a, b, and c, such that a^2 +b^2=c^2.
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
We want to use the Pythagorean Triple to find the value of x in the given triangle.
To find x, we can find a common factor of the given values. Notice that 21 and 35 are both multiples of 7.
7 * 3= 21
7 * 5= 35
Since 3, 4, 5 is a Pythagorean Triple, the missing length x must also fit this pattern.
7 * 4 = 28
We can check this by substituting these values into the Pythagorean Theorem.
28^2+ 21^2 ? = 35^2
⇕
1225=1225 âś“
