Question

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Find the length of the shonest ladder that extends from the ground to the house without touching the fence Assume the vertical wall of the house and the horirontal ground la dislance of 30 10-8-al fence nns parallel to a wall of a house have infinite extent Let L be the length of the ladder, x be the distance from the base of the ladder to the Sence, d be the distance from the fence to the house and b be the distance from the ground to the point the ladder louches the house What is the objectiver function, in terms of x? (Type an expression) The interval of interest of the objective function is (Simplity your answer Type your answer in interval nolation) The length of the shortest ladder is (Round the fnal anower to the nearest tenth as needed, Round al intermediate values to the nearest thousandh as needed) More Enter your anser in each of the answer boxes MacBook

Answer 1

ence ladder d CE (30) Let t be the o laddes fene the demce to the house be the distamce base of lad des to d be the da tanca foom the ground the ladder touchus the house bis the dis tan ce point to the d30ft A tall feme Regat Amgled toiomge (Pyagoras Theorem) Im AABC a A Ag24 Bc Foom Similan arongles A ABC amd AEDC BC DC AB BC ED ED DC h 30+x 304x LO

Sabsls tat it in 2 to 30t x Lom 1+ 100 -30+1) (+ lo0 de fManima on Miniua,d Dittwrt d( da 4(e)dBot. 2 dht100 t t00 ) HE04n) (30+x) 1opx-2 t 100 n3 -200 2 30+ n3 roo 00 +100 23 tooo t00 23 3000+ tob a3 3000 2 at n-14-42 >O IMnimun) LE Bot4 42) -> 14.421 tt50.hg