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Lina20 [59]
3 years ago
14

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?

Mathematics
2 answers:
boyakko [2]3 years ago
4 0

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:

<em>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.</em>

Base = 4 meters

Height = 3 meters

Length of the ladder = ?

<u>By Pythagoras theorem: </u>

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.

         

           

         

         

                 

                

     

vlada-n [284]3 years ago
4 0

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.

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