Question

the foot of a ladder is 10 ft out from the base of a wall. if the length of the ladder is 2 feet longer than the height of the wall where the ladder touches. how far up the wall does the ladder touch and how long is the ladder?

Answer 1

The ladder is 24 ft far up the wall and 26 ft long.

the foot of laddder=base=b=10ft

length of ladder=hypotenuse=$l$=?

height ladder up the wall=altitude=x=$l$-2 =?          (according to condition)

by using Pythagoras's theorem

        $(hypotenus)^{2}$=$(altitude)^{2}$+$(base)^{2}$

⇒       $l^{2}$=$(l-2)^{2}$+$(10)^{2}$

⇒         $l^{2}$= $l^{2}$-4$l$+100

⇒        $4l=104$

⇒        $l$=26ft

also    x=$l$-2=26-2=24ft

        putting the obtained values in Pythagoras's theorem

⇒       $(26)^{2}=(24) ^{2} +(10)^{2}$

⇒       676=100+576

⇒       676=676

        hence the given solution is correct.

To learn more about Pythagoras's theorem, click here

brainly.com/question/13188411

#SPJ4