Question

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 18 ft. Find the length of the ladder if the length is 3 ft more than its distance from the wall.

Answer 1

Answer:55.5 ft.

Step-by-step explanation:

You can start by drawing a diagram to help you understanding where everything is placed. A right triangle, where the ladder is the hypotenuse, the wall on the vertical leg, while the floor is on the horizontal leg. As stated the wall which the ladder touches is 18 ft. The length of the ladder is 3 more than the distance from the wall, so you can put the x as the distance from the wall and x+3 as the length of the ladder. Since this is a right triangle, you can use the Pythagorean’s rule (leg^2+leg^2=hypotenuse^2) to solve for x.

(18)^2 + (x)^2 = (x+3)^2 (plug in values)

324 + x^2 = x^2 + 6x + 9 (simplify)

324 = 6x + 9 (subtract x^2 )

315 = 6x (subtract 9)

x= 52.5 (divided by 6)

The answers you get is not the final answer because x is equal to the distance from the wall not the length of the ladder. Since the length is more than three feet we can add three to get our final answer.

52.5 + 3 = 55.5

Length of ladder = 55.5 ft.

Answer 2

Length of ladder is 55.5 ft.

What is Pythagoras theorem?

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let x =  distance from the wall

x + 3 = length of the ladder

Using Pythagoras theorem

$(x+3)^{2} =18^{2} +x^{2}$

$x^{2} +6x+9=324+x^{2}$

$6x = 324-9$

$6x = 315$

$x = \frac{315}{6}$

x = 52.5 ft

x + 3 = 52.5 + 3 = 55.5 ft

Length of ladder is 55.5 ft.

Find out more information about Pythagoras theorem here

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