Question

Given that x, y, and z are the lengths of the sides of a triangle, and given that x < y < z, which of the following statements is true? A. (z – y) > x B. (x + z) < y C. (x + y) > z D. (y – x) > z

Answer 1

the sum of the lengths of any 2 sides of a triangle is greater then the length of the third side

(x + y) > z <== ur answer

Answer 2

Option C

Statement
`(x+y)>z` is true

Explanation:

Given the lengths of sides of triangle are x, y, and z.

and also given that
`x<y<z`

As per the triangle inequality states that the sum of two sides of the triangle is always greater than the measure of third side.

The only condition for this triangle inequality from the given option be
`(x+y)>z`

For example:

let x= 3 unit , y= 4 unit and z= 5 unit and
`x<y<z` i,e
`3<4<5`.

then,

`(3+4)>5`

`7>5` true.

therefore, the only statement C is true.