Question

What will be the ratio of the radii of the circumcircle and the in circle of a triangle whose sides are 5, 6 and 7 cm?​

Answer 1

Answer:

Correct option is

716

Let a=4λ,b=5λ and c=6λ

Now rR=4Δrabc=4Δ2sabc[∵r=sΔ]

=4(s)(s−a)(s−b)(s−c)(4λ.5λ.6λ)(215λ)

=4(215λ)(27λ)(25λ)(23λ)900λ2=716

Answer 2

$\begin{gathered}\huge\blue{\mid{\fbox{\tt{SOLUTION}}\mid}} \\ \end{gathered}$

$Let \: a = 4 , b = 5 \: and \: c = 6$

$NOW \: \frac{R}{r} = \frac{abc}{4 {∆}^{2} } = \frac{sabc}{4∆ {}^{2} }$

$(r = \frac{∆}{s} )$

$= \frac{(4.5.6)( \frac{15}{2} )}{4(s)(s - a)(s - b)(s - c)}$

$= \frac{900 {}^{2} }{4 \frac{15}{2} ( \frac{7}{2})( \frac{5}{2} ) (\frac{3}{2} )} = \frac{16}{7}$