Question

the figure shows a triangle with side lengths a, b, and hypotenuse c.
move numbers to the table to show three side lengths that form a right triangle.

a
b
c
cm
cm
cm
2
3
4
5
7
12
25

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (longest side).

Step2: Test number combinations

• Test \(a = 3\), \(b = 4\), \(c = 5\):

\(3^2 + 4^2 = 9 + 16 = 25\), and \(5^2 = 25\). So \(3^2 + 4^2 = 5^2\).

Answer:

a: 3 cm
b: 4 cm
c: 5 cm

(Other valid Pythagorean triples could also work, but 3 - 4 - 5 is a classic example.)