msk0657 wrote:

Carcass wrote:

The distance from point X to point Y is 20 miles, and the distance from point X to point Z is 12 miles. If d is the distance, in miles, between points Y and Z. then the range of possible values for d is indicated by

(A) \(8 \leq d \leq 20\)

(B) \(8 \leq d \leq 32\)

(C) \(12 \leq d \leq 20\)

(D) \(12 \leq d \leq 32\)

(E) \(20 \leq d \leq 32\)

This is tricky.

This can be considered to a triangle.

XY = 20 ( one side)

XZ = 12 ( second one )

YZ = x (third side).

Now we need to get the value of X.

Third side = \(difference between two sides

~~\leq~~ X

~~\leq~~ sum of two sides\)

\(20 -12 \leq X \leq 20 + 12\)

=> \(8 \leq X \leq 32\)

B.

Hi @msk0657,

Please note that in a triangle following inequality holds:

Difference between two sides

< Third side

< Sum of the two sides.

In the above question, the equal sign will hold when all the points(i.e. x,y, and z) will lie on the straight line.

Thanks.