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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

#2
+73
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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
-5

From Pythagoas, c = 13/2.

Nov 18, 2020
#2
+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 $2c=15\Rightarrow c=\boxed{\frac{15}{2}}$.

MathzSolver111  Nov 18, 2020
#5
0

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

Guest Nov 19, 2020
#3
+153
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Nice work!

Nov 18, 2020
#4
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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 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