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# right-angled triangle

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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

### Best Answer

#1
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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?

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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+0 Answers

#1
+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