Learn step-by-step how to use the Pythagorean theorem to find the length of side A when you have two sides measuring 12 cm and 13 cm.
The Pythagorean theorem is a fundamental principle in geometry that applies to right-angled triangles. It states:
a² + b² = c²
where c is the hypotenuse (the longest side opposite the right angle), and a and b are the other two sides.
Step 1: Identify the sides.
You have sides of 12 cm and 13 cm. Generally, the hypotenuse is the longest side, so 13 cm is likely the hypotenuse (c).
Step 2: Set up the formula to find side A.
If we let A be one side (a) and the other known side be 12 cm (b), then:
a² + 12² = 13²
Step 3: Plug in the numbers and solve for a.
a² + 144 = 169
a² = 169 - 144
a² = 25
Step 4: Take the square root of both sides.
a = √25 = 5
Answer: Side A is 5 cm long.