Learn to Create a Robotic Device Using Arduino in the Free Webinar. Register Now
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Free webinar on Robotics (Block Chain) Learn to create a Robotic Device Using Arduino
30th Jan @ 5:00PM for Grade 1 to 10
three sides of triangle are consecutive integers and the largest angle is twice the smallest angle.the perimeter of the triangle is...? three sides of triangle are consecutive integers and the largest angle is twice the smallest angle.the perimeter of the triangle is...?
Please find the answer to your questionLet the sides of ?be n, n + 1, n + 2 where n? N.Let a = n, b = n + 1, c = n + 2 Let the smallest, angle ? A = ? then the greatest ?C = 2? In ?ABC by applying Sine Law we get, Sin ?/n = sin 2 ?/n + 2 ? sin ?/n = 2 sin ? cos ?/ n + 2 ? 1/n = 2 cos ?/n + 2 (as sin ? ? 0) ? cos ? = n + 2/2n . . . . . . . . . . . . . . . . . . . . . . . . . (1) In ? ABC by Cosine Law, we get Cos ? = (n + 1)2 + (n + 2)2 – n2/2(n + 1) (n + 2) . . . . . . . . . . . . . . . . . . . (2) Comparing the values of cos ? from (1) and (2), we get (n + 1)2 + (n + 2)2 – n2/2(n + 1) (n + 2) = n + 2/2n ? (n + 2)2 (n + 1) = n(n + 2)2 + n(n + 1)2 – n3 ? n (n + 2)2 (n + 2)2 = n(n + 2)2 + n(n + 1)2 – n3 ? n2 + 4n + 4 = n3 + 2n2 + n – n3 ? n2 – 3n – 4 = 0 ? (n + 1) (n – 4) = 0 ? n = 4 (as n ? - 1) ? Sides of ? are 4, 4 + 1, 4 + 2, i.e. 4, 5, 6.
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -