Question

Can someone please help me with this multiple choice question?

Answer 1

17.
Since we know the hypotenuse and a leg, we can find the scale factor and determine x.
The scale factor is
18 ÷ 8 = 2.25
Now we break up the hypotenuse
2.25x = 24
|
{2.25x = 24} ÷ 2.25
|
x = 10 and 2/3
The answer is therefore B

18.
We can eliminate C. EDC because it is not a right angle first off.
Now we can start eliminating the rest
B. ABD has the same height but different base and hypotenuse so that can be crossed off.
D. DBC does not have a right angle either so it can be crossed off as well.
This leaves us with A. EBD, our answer.
EBD has a right angle, similar looking legs, and a similar hypotenuse so therefore it is the correct answer.

I really hope that this helps. If not, I hope you find the answer!

Answer 2

1) the small and large triangles are similar, then we can write:

x/24 = 8/18
Cross multiplication → 18x = 24.8 → 18x = 192 and x = 192/18

and x = 32/3 Or 10 ²/³

2) Δ ABC is similar to Δ EDC Since:

∠A = ∠D = 90°

∠C is common