One side of a triangle is 5 cm longer than twice another side the ray bisecting an angle formed by the sides divides the opposite side into six and 15 cm segment find the perimeter of the triangle

Answer 1

s1 = 5+2s2

(6+15)^2 = (x+5)^2 + x^2

21^2 = x^2 +10x +25 +x^2

441-25 = 416 = 2x^2 +10x

208 = x^2 + 5x

208+ 25/4 = x^2 +5x + 25/4

214 1/4 = (x+ 5/2)^2

+ or -14.64 = x+ 2.5

x = 12.14 or -17.14, ignore the negative solution

Perimeter = 21 + 12.14 + 17.14 = 50.28 cm

Answer 2

Let one side is x, then other side is (2x + 5). So by property of bisector we have proportion: x/6 = (2x + 5)/15;

15x = 6(2x + 5); or 5x = 4x + 10; x = 10 cm.

So sides of triangle: 10, 25 and 21 cm and perimeter P = 10 + 25 + 21 = 56 cm