Alan

I've looked more carefully in the book at the equations and the diagram from which they are derived, and I can see that the second equation has a misprint (in the book). The term (100 - V2)/30 should be (100 - V3)/30.  

With this change the solutions given for V2 and V3 in the book are correct.

According to Wikipedia:

Actually rosala, question 1 is false, because ">" doesn't mean "not equal to", it means "greater than".  Since 18 isn't greater than 19, then b+10>19 is false when b = 8.

You are right that the answer to question 2 is true; however, note that it is an equality, not an inequality.

You are right in thinking this is hard DragonSlayer554!  Far too hard to do by hand, so I've used the numerical solution capabilities of some technical software to do it:

You're right Chris, there is some double counting in the way I did it!

See Chris's calculations below.

You're welcome!

tan(45°) is 1, so the vertical line above Z must be of length 9 for this to be true. This means WX also has length 9.  The line VZ is √(9²+9²) = 9√2 from Pythagoras.  The length of the perimeter is therefore given by:

$${\mathtt{9}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{9}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{9}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{2}}}} = {\mathtt{42.727\: \!922\: \!061\: \!357\: \!855\: \!4}}$$

or 42.73 to two decimal places.

The whole circumference is given by 2*pi*25.  The shorter arc length from B to C is the fraction 144/360 of the whole circumference (because there are 360° needed to go all the way around the circumference, and you just want to go 144° around), namely:

$${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{25}}{\mathtt{\,\times\,}}{\mathtt{144}}}{{\mathtt{360}}}} = {\mathtt{62.831\: \!853\: \!071\: \!795\: \!864\: \!8}}$$

or ≈ 62.8