The diameter of the circumcircle of a triangle with sides 5 cm, 6 cm and 7 cm is?

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\frac{3 \sqrt 6}{2}

\sqrt

6cm

\frac{35}{48} cm

None of these

answer is D.

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Detailed Solution

Concept- The circle has three sides, measuring 5 cm, 6 cm, and 7 cm, as is obvious. As a result, we obtain a = 5, b = 6, and c =7.
We will start by determining the triangle's semi-perimeter value.
The result of changing the values of a, b, and c in the

s = \frac{5 + 6 + 7}{2} .

We obtain s=

\frac{18}{2}

by adding the items in the numerator.
18 divided by 2 gives us s=9.
We will now calculate the triangle's area value.
The formula A=s(s-a)(s-b)(s-c) is changed to

A = \sqrt 9 (9 - 5) (9 - 6) (9 - 7)

by substituting s=9, a=5, b=6, and c=7.
A= 9

\times

\times

\times

2 is obtained by taking the terms in the brackets out.
When we multiply the terms, we obtain A=

\sqrt

216=6.
We shall now calculate the triangle's circumradius.
R=

\frac{5 \times 6 \times 7}{4 (6 \sqrt 6)}

is obtained by replacing

A = 6 \sqrt 6, a = 5, b = 6, and c = 7

in the formula R=

\frac{a \times b \times c}{4 a}

.
By condensing the terms, we obtain R=

\frac{35}{4 \sqrt 6}

.
We are aware that the circle's radius is equal to half of its diameter. To determine the triangle's circumcircle's diameter, we will multiply the circumradius by two.
Triangle's circumcircle's diameter is equal to 2R.
By changing R in the previous equation to =