Respuesta :
Answer:
The lengths of the three sides are 10 cm, 9.49 cm and 3.16 cm
Step-by-step explanation:
Let
c ------> the length of the hypotenuse of a right triangle
x -----> the length of one leg
y -----> the length of the other leg
we know that
[tex]c^{2}=x^{2}+y^{2}[/tex] -----> equation A (Pythagoras Theorem)
[tex]c=10\ cm[/tex] ----> equation B
[tex]x=3y[/tex] -----> equation C
Substitute equation B and equation C in equation A and solve for y
[tex]10^{2}=(3y)^{2}+y^{2}[/tex]
[tex]100=10y^{2}[/tex]
[tex]y^{2}=10[/tex]
[tex]y=\sqrt{10}\ cm[/tex]
[tex]y=3.16\ cm[/tex]
Find the value of x
[tex]x=3(\sqrt{10})=9.49\ cm[/tex]
therefore
The lengths of the three sides are 10 cm, 9.49 cm and 3.16 cm
The lengths of the three sides of the triangle are;
Hypotenuse = 10 cm
First leg = 3.162 cm
Second leg = 9.486 cm
Further Explanation:
Right triangle
- A right triangle is a triangle with one of its angles being 90 degrees or right angle.
- The triangle has two shorter sides making the right angle and the hypotenuse which is the longest side.
Pythagoras Rule
- According to Pythagoras rule, in a right angled triangle if the squares of the shorter sides are added then they are equivalent to the square of the hypotenuse.
- That is;[tex]a^{2} +b^{2} =c^{2}[/tex] , where a and b are the shorter sides while c is the hypotenuse.
In this case;
We are given;
Hypotenuse = 10 cm
First leg = [tex]x cm[/tex]
second leg = [tex]3x cm[/tex]
Therefore;
a = x cm
b = 3x cm
c = 10 cm
Hence;
[tex]x^{2} +(3x)^{2} =10^{2}[/tex]
[tex]x^{2} + 9x^2 = 100[/tex]
[tex]x^{2} + 9x^2 =100[/tex]
Solving for x
[tex]10x^{2} =100\\x^{2}=10\\x = \sqrt{10} \\x= 3.162[/tex]
Therefore;
x = 3.162 cm
hence;
The lengths of the three sides of the triangle are;
Hypotenuse = 10 cm
First leg = 3.162 cm
Second leg = 9.486 cm
Keywords: Right triangle, Pythagoras rule
Learn more about:
- Pythagoras theorem: https://brainly.com/question/4098846
- Right triangle: https://brainly.com/question/4098846
Level; High school
Subject: Mathematics
Topic: Pythagoras theorem
