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A right triangle has legs of length $6$ and $b,$ and a hypotenuse of length $c$. The perimeter of the triangle is $18$. Compute $c$.

 Nov 18, 2020

Best Answer 

 #2
avatar+73 
+2

I found the correct answer. Your answer is wrong but thanks for trying. 

This is the explanation for the real answer :

 

Since the perimeter is $18$, $b+c=12$. Also, by the Pythagorean Theorem, $c^{2}-b^{2}=6^{2}$. Thus,
                                                             $36=c^{2}-b^{2}=(c-b)(c+b)=12(c-b)$
So $c-b=3$. Adding $b+c=12$ to this, we find $2c=15\Rightarrow c=\boxed{\frac{15}{2}}$.

 Nov 18, 2020
 #1
avatar
-5

From Pythagoas, c = 13/2.

 Nov 18, 2020
 #2
avatar+73 
+2
Best Answer

I found the correct answer. Your answer is wrong but thanks for trying. 

This is the explanation for the real answer :

 

Since the perimeter is $18$, $b+c=12$. Also, by the Pythagorean Theorem, $c^{2}-b^{2}=6^{2}$. Thus,
                                                             $36=c^{2}-b^{2}=(c-b)(c+b)=12(c-b)$
So $c-b=3$. Adding $b+c=12$ to this, we find $2c=15\Rightarrow c=\boxed{\frac{15}{2}}$.

MathzSolver111  Nov 18, 2020
 #5
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0

c - b = 3    where did you get it from?

Guest Nov 19, 2020
 #3
avatar+153 
0

Nice work!

 Nov 18, 2020
 #4
avatar+1440 
+3

A right triangle has legs of length 6 and b and a hypotenuse of length c.The perimeter of the triangle is18.Compute c.

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

a = 6               b = 6 / tanA              c = sqrt[62 +(6 / tanA)2]

 

We'll use this information to calculate the angle A       a + b + c = 18

 

6 + 6 / tanA + sqrt[62 + (6 / tanA)2] = 18                angle A = 53.13010235º

 

Side  b = 6 / tanA = 4.5

 

Side  c = sqrt(a2 + b2) = 7.5

 

 Nov 18, 2020
edited by Dragan  Nov 18, 2020

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