Question

(05.02)One triangle on a graph has a vertical side of 5 and a horizontal side of 11. Another triangle on a graph has a vertical side of 15 and a horizontal side of 33.

Could the hypotenuses of these two triangles lie along the same line?

No, because they need to be the same size
No, because they are not similar triangles
Yes, because all triangles can fit along this line
Yes, because they are similar triangles

Answer 1

yes because they are similar triangles

Answer 2

The answer is the option

Yes, because they are similar triangles

Explanation:

we know that

The first and the second triangle are right triangles

The hypotenuses of these two triangles could lie along the same line, if the two triangles were similar

Verify if the triangles are similar

Remember that

If two triangles are similar then

the ratio of their corresponding sides is equal

so

`(5)/(15)=(11)/(33)`

simplify

`(1)/(3)=(1)/(3)` --------> is rue

therefore

the triangles are similar

and the answer is

Yes, because they are similar triangles