The Warrens live on a corner lot Often children cut across t

The Warren\'s live on a corner lot. Often, children cut across their lot to save walking distance. Given the diagram, find how many feet of walking distance is saved by cutting across the property instead of walking around the lot. Long side: 51 feet Other side: x+21 Other side: x The walking distance that is saved by cutting across the lot is ? feet.

Solution

When Children cut across a corner lot, a right angled triangle is formed. Since the hypoteuse is 51 feet and the other sides are x ft and x + 21 ft., hence by Pythagoras theorem, 51² = x²+(x+21)² = x² + x²+42x + 21² or, 2x²+42x +441- 2601 = 0 or, 2x²+42x - 2160 = 0 or, x² +21x - 1080 = 0 or, on using the quadratic formula, x = [-42± { 42² -4*1*(-1080)]/2*1 = [ -42 ± ( 1764+ 4320)]/2 = [-42± 6084]/2 = (-42± 78)/2. Since x cannot be negative, we have x =( -42+78)/2= 36/2 = 18. Then. the distance saved is x+x +21 - 51 = 2x+21-51 = 36 +21 -51 = 57-51 = 6 ft. .