Medium Puzzles 

Workings

Hint
You might find Pythagoras' theorem very useful [a² + b² = c²].

Answer
148 inches.



We can use Pythagoras' theorem if we draw an imaginary line across to create a right-angled triangle.

The hypotenuse is equal to the rope's length R. The bottom of the triangle is 48 inches. The vertical side is R - 8 (the difference between 20 inches and 12 inches).

Pythagoras' theorem tells us that:

   a² + b² = c²

Where c is the hypotenuse.

This gives us:

          48² + (R - 8)² = R²

   2304 + (R - 8)(R - 8) = R²

    2304 + R² - 16R + 64 = R²

         2304 - 16R + 64 = 0

                     16R = 2368

                       R = 148

As required.

Workings

Hint
The first letters of the words are: W, E, S, A, S, C, O, T, W, A.

Answers
Windbreak, eiderdown, sometimes, afternoon, September, carpenter, offensive, telephone, Wednesday, apartment.
win + dbr + eak = windbreak
eid + erd + own = eiderdown
som + eti + mes = sometimes
aft + ern + oon = afternoon
sep + tem + ber = september
car + pen + ter = carpenter
off + ens + ive = offensive
tel + eph + one = telephone
wed + nes + day = wednesday
apa + rtm + ent = apartment

Workings

Hint
The first word begins with the letter J.

Answers
-e-el  = jewel  (JW) b-d    = bad    (A) s-i-l  = skill  (KL) swa--  = swaps  (PS) fo-    = fox    (X) -er-y  = ferry  (FR) a-ur-  = azure  (ZE) -u-dy  = buddy  (BD) -uo-e  = quote  (QT) -e-a-e = menace (MNC) ed--   = edgy   (GY) sc-r-y = scurvy (UV) l-p    = lop    (O) --lls  = hills  (HI)
There is at least 1 more answer, can you find another?

Newel, bad, shill, swaps, fox, jerky, azure, ruddy, quote, became, edgy, scurvy, lop, fills.

Workings

Hint
The first word is ONE.

Answer
One good turn deserves another.