Answer:
Option 2 - 3.2 inches.
Step-by-step explanation:
Given : The lengths of two sides of a right triangle are 5 inches and 8 inches.
To find : What is the difference between the two possible lengths of the third side of the triangle?
Solution :
According to question, it is a right angle triangle
Applying Pythagoras theorem,
[tex]H^2=P^2+B^2[/tex]
Where, H is the hypotenuse the longer side of the triangle
P is the perpendicular
B is the base
Assume that H=8 inches and B = 5 inches
Substitute the value in the formula,
[tex]8^2=P^2+5^2[/tex]
[tex]64=P^2+25[/tex]
[tex]P^2=64-25[/tex]
[tex]P^2=39[/tex]
[tex]P=\sqrt{39}[/tex]
[tex]P=6.24[/tex]
Assume that P=8 inches and B = 5 inches
Substitute the value in the formula,
[tex]H^2=8^2+5^2[/tex]
[tex]H^2=64+25[/tex]
[tex]H^2=89[/tex]
[tex]H=\sqrt{89}[/tex]
[tex]H=9.43[/tex]
Therefore, The possible length of the third side of the triangle is
[tex]L=H-P[/tex]
[tex]L=9.43-6.24[/tex]
[tex]L=3.19[/tex]
Therefore, The difference between the two possible lengths of the third side of the triangle is 3.2 inches.
So, Option 2 is correct.
Answer: B. 3.2 inches
Step-by-step explanation: I took the test and i got it right
