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A right-angled triangle has a perimeter of 1276 and a longest side of 533.  What is the length of the inradius?

 Feb 8, 2021

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A right-angled triangle has a perimeter of 1276 and the longest side of 533.  What is the length of the inradius?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Side:       c = 533

 

(743 - a)2 + a2 = 5332

 

a = 308

 

b = 743 - 308 = 435

 

Semiperimeter:     s = 1276 / 2 = 638

 

Triangle area:        A = 1/2(308 * 435) = 66990

 

Inradius:            r = A / s = 105

 Feb 8, 2021
edited by jugoslav  Feb 8, 2021
 #1
avatar+1300 
+3
Best Answer

A right-angled triangle has a perimeter of 1276 and the longest side of 533.  What is the length of the inradius?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Side:       c = 533

 

(743 - a)2 + a2 = 5332

 

a = 308

 

b = 743 - 308 = 435

 

Semiperimeter:     s = 1276 / 2 = 638

 

Triangle area:        A = 1/2(308 * 435) = 66990

 

Inradius:            r = A / s = 105

jugoslav Feb 8, 2021
edited by jugoslav  Feb 8, 2021

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