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castortr0y [4]
3 years ago
5

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 88 feetfeet less than th

e length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 1616 feet.
Mathematics
1 answer:
Y_Kistochka [10]3 years ago
4 0

Answer: The length of the ladder is 20 feet.

Step-by-step explanation:

Given : A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 8 feet less than the length of the ladder.

Mathematically,

Let x be the length of the ladder then

Distance from ground to the top of the ladder = x- 8

If distance from the bottom of the ladder to the building is 16 feet.

Since ground makes right angle with building , so the triangle made by ladder should be a right triangle.

By Pythagoras theorem of right triangle , we hae

(Hypotenuse)=(Perpendicular)^2+(Base)^2

\Rightarrow\ x^2=(x-8)^2+16^2\\\\\Rightarrow\ x^2=x^2+64-16x+256\ [\text{Using identity :} (a-b)^2=a^+b^2-2ab]\\\\\Rightarrow 0=-16x+320\\\\\Rightarrow\ 16x=320\\\\\Rightarrow\ x=\dfrac{320}{16}=20

Hence, the length of the ladder is 20 feet.

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