Question

Mr. Dyer is leaning a ladder against the side of his house to repair the roof. The top of the ladder reaches the roof, which is 3 meters high. The base of the ladder is 4 meters away from the house, where Mr. Dyer's son is holding it steady. How long is the ladder?

Answer 1

The height of the ladder is 5 m.

Step by Step Explanation:

We have drawn diagram for your reference.

Given:

Distance of roof from base of the house = 3 m.

According to diagram;

AB = 3 m

Distance of the base of the ladder from the house = 4 m

According to diagram;

BC = 8 ft

We need to find the height of the ladder AC.

Solution:

Let us consider the scenario to be a right angled triangle with right angle at B.

So we will use Pythagoras theorem.

"In a right angle triangle square of sum of 2 sides is equal to square of the third side."

framing in equation form we get;

`AC^2=AB^2+BC^2`

Substituting the given values we get;

`AC^2=3^2+4^2\\\\AC^2=9+16\\\\AC^2=25`

Taking Square root on both side we get;

`√(AC^2)=√(25)\\\\AC=5\ m`

Hence The height of the ladder is 5 m.

Answer 2

5 meters.

Explanation:

Given:

Mr. Dyer is leaning a ladder against the side of his house to repair the roof.

The top of the ladder reaches the roof, which is 3 meters high.

The base of the ladder is 4 meters away from the house, where Mr. Dyer's son is holding it steady.

Question asked:

How long is the ladder?

Solution:

Here we found that a right angle triangle is formed in which base and height is given and we have to find the longest side of the triangle.

Base = 4 meters

Height = 3 meters

Length of the ladder = ?

By Pythagoras theorem:

Square of longest side = Square of base + Square of height

`(Longest\ side)^(2) = 4^(2) +3^(2)`

`(Longest\ side)^(2) = 16+9`

`(Longest\ side)^(2) = 25`

Taking root both side :-

`\sqrt[2]{(Longest\ side)^(2) } =\sqrt[2]{25}`

`Longest\ side = \sqrt[2]{5*5} \\ Longest\ side = 5`

Thus, length of ladder is 5 meters.