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

Answer:

5 meters.

Step-by-step 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 :-        

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

 $Longest\ side = \sqrt[2]{5\times5} \\ Longest\ side = 5$

Thus, length of ladder is 5 meters.

         

           

         

         

                 

                

     

Answer 2

Answer:

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;

$\sqrt{AC^2}=\sqrt{25}\\\\AC=5\ m$

Hence The height of the ladder is 5 m.