Question

Triangles ABC and DEF are similar.

What is the length of DE ?













A.
15 cm







B.
21 cm







C.
24 cm







D.
27 cm

Answer 1

@e.mccormick Can you please help me?

Answer 2

@marziajackson$ Similar triangles have the same angles, but the lengths are different. To keep the same angle, the relative ratios between the sides must be equal.

You can see this when we look at a triangle like a 3,4,5 triangle with 5 being the hypotenuse. Look at a 6,8,10 triangle.

If solve for x and we bust out our trig saying SOA CAH TOA \[sin x = opposite/adjacent\]\[cos x =adjacent/hypotenuse\]\[tan x = opposite/adjacent\]

If we do COA for both we have \[cos x =3/5\] and \[cos x = 6/10\] I think you can see that 3/5 and 6/10 are the same.