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The hypotenuse of a right triangle is 37 units long. Find the other two sides if the perimeter of the triangle is 84 units.

 Mar 30, 2020
 #1
avatar+23540 
0

35    and  12   work       by brute force

 Mar 30, 2020
 #3
avatar+626 
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Please don't just provide an answer without showing your work. I recommend not using brute force as a method too.

AnExtremelyLongName  Mar 30, 2020
 #2
avatar+626 
+2

Leg a = \(a\)

Leg b = \(b\)

 

By perimeter:

\(a + b+37=84\)

\(a+b=47\)

 

By Pythagorean Theorem:

\(a^2+b^2=37^2\)

 

Substitution:
\(a^2+(47-a)^2=37^2\)

 

Solving:

a^2+(47-a)^2=37^2 = {a=12, a=35}

 

a = 12

b = 35

 

or

 

a = 35

b = 12

 Mar 30, 2020

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