Question

Find the value of x to the nearest tenth.

60.0
15.5
39.0
31.0

Answer 1

is there some sort of equation?

Answer 2

use the property of similar triangles that corresponding sides are proportional. \[2x:62 = 39:(39+39) = 49:(49+49)\]Do the work carefully — there's a "trap" answer waiting for you that will be very tempting!

Answer 3

thank @whpalmer4

Answer 4

Did you get an answer yet?

Answer 5

it is 39.0

Answer 6

No :-(

Maybe the ratio notation threw you off, I'll do it as fractions instead:

\[\frac{2x}{62} = \frac{39}{39+39} = \frac{49}{49+49} = \frac{1}{2}\]

Answer 7

so it is 15.5 then

Answer 8

It couldn't be 39.0 — all of the other sides double when going from the small triangle to the big triangle, and 62 is not a doubling of 39.

Answer 9

Yes, 15.5 is correct. The trap answer of 31 is also in the answer choices, to catch those who see that there's a ratio of 1:2 between the sides, but fail to notice that the problem calls the small side "2x" instead of "x" :-)

Answer 10

sweet thanks you so much i was lost on how to set the problem up

Answer 11

you're welcome.

Answer 12

Which lines can you conclude are parallel given that M<7 + M<11 =180? Justify your conclusion with a theorem.
Line a is parallel to line b by the Converse of the Alternate Interior Angles Theorem.
Line c is parallel to line d by the Converse of the Same-Side Interior Angles Theorem.
Line a is parallel to line b by the Converse of the Same-Side Interior Angles Theorem.
Line c is parallel to line d by the Converse of the Alternate Interior Angles Theorem.