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
12, 35, 37
12^2+ 35^2= 37^2
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 24 and 74 are both multiples of 6.
2 * 12= 24
2 * 37= 74
Since 12, 35, 37 is a Pythagorean Triple, the missing length x must also fit this pattern.
2 * 35 = 70
We can check this by substituting these values into the Pythagorean Theorem.
24^2+ 70^2 ? = 74^2
⇕
5476=5476 âś“
