Question

Select all the sets of the value that could be the side length of Triangle z.sides are 7,4,10

Answer 1

We will determine if the sets are proportional, if they are, then those will be the sets of lengths that would belong to triangle z, that is:

a.

`(4)/(8)=(7)/(11)=(14)/(10)\Rightarrow(1)/(2)\\e(7)/(11)\\e(7)/(5)`

So, set a is not one.

b.

`(4)/(10)=(7)/(17.5)=(10)/(25)\Rightarrow(2)/(5)=(2)/(5)=(2)/(5)`

So, set b could be a set of lengths that belong to triangle z.

c.

`(4)/(6)=(7)/(9)=(10)/(11)\Rightarrow(2)/(3)\\e(7)/(9)\\e(10)/(11)`

So, set c is not one.

d.

`(4)/(6)=(7)/(10.5)=(10)/(15)\Rightarrow(2)/(3)=(2)/(3)=(2)/(3)`

So, set d could be a set of lengths that belong to triangle z.

e.

`(4)/(8)=(7)/(14)=(10)/(20)\Rightarrow(1)/(2)=(1)/(2)=(1)/(2)`

So, set e could be a set of lengths that beling to triangle z.

So, the options that could be candidate are: b, d & e.