+0  
 
0
81
2
avatar

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

 Jul 25, 2021
 #1
avatar+121056 
+2

inradius ,  r   for  a right triangle  =

 

[  sum  of two  leg  lengths  -  hypotenuse  ]    /   2

 

The  sum of  the two  leg lengths =   1276  -  533  =  743

 

So

 

r  =    [ 743  - 533  ]  /  2    =     210  / 2  =  105

 

cool cool cool

 Jul 25, 2021
 #2
avatar+1496 
+2

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

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

P = 1276          s = 1276 / 2           Hypotenuse c = 533

 

Short leg = a         long leg = b            a + b = 743

 

a2 + (743 - a)2 = c2

 

a = 308           b = 435

 

A = 1/2(ab)

 

Inradius     r = A / s = 105

 Jul 25, 2021

41 Online Users

avatar