It looks like you've uploaded a page with a few geometric problems. Let me help you analyze the work shown in the image and guide you through the steps to calculate the unknowns in the given triangles.

The questions appear to involve the use of the Pythagorean theorem and the properties of right triangles. Let's go through each part:

a) Triangle with sides 8 cm and 3 cm, where the unknown side is $x$:

The Pythagorean theorem is applied, where: $x^2 = 8^2 + 3^2$ Solving for $x$, we get: $x^2 = 64 + 9 = 73$ $x = \sqrt{73} \approx 8.54 \, \text{cm}$

b) Triangle with sides 40 cm and 13 cm, and an unknown side $x$:

This triangle also seems to be a right triangle, so applying the Pythagorean theorem: $x^2 = 40^2 + 13^2$ $x^2 = 1600 + 169 = 1769$ $x = \sqrt{1769} \approx 42.05 \, \text{cm}$

c) Triangle with legs 2 m and 3 m, hypotenuse given as $9.1$ m:

The Pythagorean theorem gives: $9.1^2 = 2^2 + 3^2$ $82.81 = 4 + 9 = 13$ So it seems like there may have been a mistake or confusion in solving this triangle in the work you've written (for example, $9.1^2$ should be 82.81, not the sum of 2 and 3).

Would you like to go over these steps in more detail or clarify the results further?