A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s. A) A(s) = 2s 144 - s2 B) A(s) = s 144 - s2 C) A(s) = 2s 12 - s2 D) A(s) = 12s 144 - s2 10) The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)? A) 12 ft B) 13 ft C) 14 ft D) 15 ft

• calculista: Part a)
  we know that
  area of triangle=b*h/2
  b=s
  applying the Pythagoras theorem
  h²=12²-s²--------> h=√(144-s²)
  so
  A=(1/2)*s*√(144-s²)
  Part b)
  applying the Pythagoras theorem
  c²=a²+b²
  in this problem
  c is the minimum length ladder needed to reach the top of the wall
  a=5 ft
  b=13 ft
  so
   c²=5²+13²-----> c²=194--------> c=13.93 ft-------> c=14 ft
  
  the answer is 
  14 ft