If the sides of a triangle are consecutive integers and the maximum angle is twice the minimum, determine the sides of the triangle.


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 76112 by Maclaurin Stickker last updated on 23/Dec/19

$I f t h e s i d e s o f a t r i a n g l e a r e c o n s e c u t i v e$ $i n t e g e r s a n d t h e m a x i m u m a n g l e$ $i s t w i c e t h e m i n i m u m, d e t e r m i n e$ $t h e s i d e s o f t h e t r i a n g l e .$
	Answered by mr W last updated on 24/Dec/19

	$s a y t h e s i d e s a r e n - 1, n, n + 1$ $\cos θ_{m a x} = \frac{{(n - 1)}^{2} + n^{2} - {(n + 1)}^{2}}{2 (n - 1) n} = \frac{n - 4}{2 (n - 1)}$ $\cos θ_{m i n} = \frac{{(n + 1)}^{2} + n^{2} - {(n - 1)}^{2}}{2 (n + 1) n} = \frac{n + 4}{2 (n + 1)}$ $θ_{m a x} = 2 θ_{m i n}$ $\cos θ_{m a x} = 2 \cos^{2} θ_{m i n} - 1$ $\frac{n - 4}{2 (n - 1)} = 2 \times \frac{{(n + 4)}^{2}}{4 {(n + 1)}^{2}} - 1$ $\frac{n - 4}{n - 1} = \frac{4 n + 14 - n^{2}}{n^{2} + 2 n + 1}$ $2 n^{3} - 7 n^{2} - 17 n + 10 = 0$ $(n + 2) (n - 5) (2 n - 1) = 0$ $\Rightarrow n = 5$ $\Rightarrow s i d e s a r e 4, 5 a n d 6 .$
	Commented by Maclaurin Stickker last updated on 24/Dec/19

	$I d i d b y t h e s a m e w a y, b u t I {w a s n}^{'} t$ $s u r e . T h a n k y o u f o r t h e g r e a t$ $a n s w e r .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum