Final answer:
To find the third side of similar triangles, we use the ratio of corresponding sides. For right-angled triangles, the Pythagorean theorem is used, following the formula a² + b² = c² to solve for the missing side.
Step-by-step explanation:
The student's question involves similar triangles and finding the lengths of missing sides. Since the triangles are similar, their corresponding sides are in the same ratio. To find the length of the third side of each triangle, we can use the properties of similar triangles if the ratio of two corresponding sides are given. If the triangles are right-angled, we can also use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem is mathematically expressed as a² + b² = c² where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
To solve for the third side of right-angled triangles using the Pythagorean theorem, rearrange the formula to solve for the desired side. For example, if the lengths of the legs (a and b) are given and you need to find the hypotenuse (c), you use c = √(a² + b²). Conversely, if you have the hypotenuse and one leg and need to find the other leg, you would rearrange the formula accordingly.