Read it again any time, including while you work through the exercises.
Here is probably the most famous theorem in the world! It is about right triangles, those with a right angle. In such a triangle, the side opposite the right angle is called the hypotenuse: it is always the longest of the three sides. Spot it carefully, the whole theorem revolves around it.
The Pythagorean theorem states: in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. As a formula, if the hypotenuse is c and the other two sides are a and b, then a² + b² = c². Picture it: draw a square on each side of the triangle; the area of the big square (on the hypotenuse) is exactly the sum of the areas of the two smaller ones!
What is it for? Computing an unknown length without measuring it. You know two sides of a right triangle? The third one can be calculated: square, add (or subtract if you want a short side), then take the square root. Builders have used it for millennia to check right angles with the famous 13-knot rope (the 3, 4, 5 triangle).
The theorem also works in reverse: that is the converse. If the lengths of a triangle satisfy a² + b² = c², then the triangle is right-angled, and the right angle faces the longest side c. Handy for proving an angle is right without a set square!
One last tip: when the result is not a perfect square, the square root gives a never-ending decimal. You then round the answer, for example to the nearest tenth, as asked in the problem.