In a right- angled triangle, one side is 8.3cm and another is 7.7. How do you find the perimeter of the triangle?

1 Answer
Mar 26, 2018

Answer:

Two cases:

#27.32 \ "cm"#

#19.1 \ "cm"#

Explanation:

I see two cases in the following problem.

CASE 1: FINDING THE HYPOTENUSE

Let's say that you need to find the hypotenuse #c#, of the right-angled triangle.

Using Pythagoras' theorem, we got:

#a^2+b^2=c^2#

And so,

#8.3^2+7.7^2=c^2#

#c^2=128.18#

#c=sqrt(128.18)#

#=11.32#

Therefore, the perimeter will be #11.32+8.3+7.7=27.32# centimeters.

CASE 2: FINDING THE OTHER LEG

If the hypotenuse is already given, in this case, #8.3 \ "cm"#, we can easily find the other leg.

Using Pythagoras', #a^2+b^2=c^2#

#a^2=c^2-b^2#

Substitute in given values,

#a^2=8.3^2-7.7^2#

#=9.6#

#a=sqrt(9.6)#

#~~3.1#

And so, the perimeter here will be #3.1+8.3+7.7=19.1# centimeters.