Respuesta :
Answer:
10.2 inches
Step-by-step explanation:
Ok let's assume we don't know the larger (the c value).
So this means using [tex]a^2+b^2=c^2[/tex] we have:
[tex]12^2+15^2=c^2[/tex]
[tex]144+225=c^2[/tex]
[tex]369=c^2[/tex]
Square both sides:
[tex]c=\sqrt{369} \aprox 19.2[/tex
Now assume we know the larger is 15 (this means c=15 now), then we have
[tex]a^2+12^2=15^2[/tex]
[tex]a^2+144=225[/tex]
Subtract 144 on both sides:
[tex]a^2=225-144[/tex]
Simplify:
[tex]a^2=81[/tex]
Square root both sides:
[tex]a=9[/tex]
The difference between 19.2 and 9 is 19.2-9=10.2.
Answer:
Option 1 - 10.2 inches.
Step-by-step explanation:
Given : The lengths of two sides of a right triangle are 12 inches and 15 inches.
To find : What is the difference between the two possible lengths of the third side of the triangle?
Solution :
Since, It is a right angle triangle so we apply Pythagoras theorem,
[tex]C^2=A^2+B^2[/tex]
Where, C is the hypotenuse the longer side of the triangle
A is the perpendicular
B is the base
There will be two cases,
1) Assume that C=15 inches and B = 12 inches
Substitute the value in the formula,
[tex]15^2=A^2+12^2[/tex]
[tex]225=A^2+144[/tex]
[tex]A^2=225-144[/tex]
[tex]A^2=81[/tex]
[tex]A=\sqrt{81}[/tex]
[tex]A=9[/tex]
Assume that A=15 inches and B = 12 inches
Substitute the value in the formula,
[tex]C^2=15^2+12^2[/tex]
[tex]C^2=225+144[/tex]
[tex]C^2=369[/tex]
[tex]C=\sqrt{369}[/tex]
[tex]C=19.2[/tex]
Therefore, The possible length of the third side of the triangle is
[tex]L=C-A[/tex]
[tex]L=19.2-9[/tex]
[tex]L=10.2[/tex]
Therefore, The difference between the two possible lengths of the third side of the triangle is 10.2 inches.
So, Option 1 is correct.