Question

In triangle XYZ , measure of angle x :measure of angle y: measure of angle z =1:2:3 .If XY =15,YZ= ?

Answer 1

xy=15
And ratio of x & y = 1:2
So, X = 5 and y = 10
Ratio of y to z = 2:3
So, if y = 10, z= 15
Therefore YZ=10+15=25

Answer 2

ratio of all three angles = 1:2:3

let then be x , 2x and 3x respectively

using angle sum property of triangle
x+ 2x + 3x = 180
6x = 180
x = 30°

angle x = 30°
2x = 30 × 2 = 60 °
3x = 30 × 3 = 90°

now,
we know that it's a right angled traingle,
so by using pythagoras theorem,

(XZ)^2 +(ZY)^2 =(XY)^2

(XZ)^2 +(ZY)^2 =(15)^2

(XZ)^2 +(ZY)^2 =225

(ZY)^2 =225 - (XZ)^2
YZ = root {225 -( XZ)^2}