ΔABC and ΔDEF are similar. Find the values of x and y.
Triangle ABC is shown with side AB labeled y, side BC labeled 12, and side CA labeled 21. Triangle DEF is shown with side DE labeled 6, EF labeled 4, and FD labeled x.
A. x = 7, y = 12
B. x = 21, y = 12
C. x = 14, y = 18
D. x = 7, y = 18
The answer is D x=7 and y=18
Divide 12 by 4 to get 3
10 multiply 6× 3 to get Y
Then divide 21 by 3 to get X
Your welcome 😌
@Me right is correct, Thx
DE/AB = 6/y
EF/BC = 4/12 = 1/3
FD/CA = x/21
Now you know that all three ratios are the same, so just solve
6/y = 1/3
x/21 = 1/3
hello! finally introducing.. LOOΠΔ! are you girls ready? okay.. let's go!
To find the values of x and y, we need to use the concept of similar triangles.
Similar triangles have proportional sides. By comparing the corresponding sides of ΔABC and ΔDEF, we can set up the following ratios:
AB/DE = BC/EF = CA/FD
Let's substitute the given values into this ratio:
y/6 = 12/4 = 21/x
Simplifying this ratio, we have:
y/6 = 3 = 21/x
To find the value of y, we can cross multiply:
(y)(x) = (6)(3)
yx = 18
To find the value of x, we can divide both sides of the equation by y:
x = 18/y
Now, let's check the answer choices:
A. x = 7, y = 12
Substituting the values, we get:
7 ≠ 18/12
Therefore, A is not the correct answer.
B. x = 21, y = 12
Substituting the values, we get:
21 ≠ 18/12
Therefore, B is not the correct answer.
C. x = 14, y = 18
Substituting the values, we get:
18/6 = 12/4 = 21/14
This simplifies to:
3 = 3 = 3
Therefore, C is the correct answer.
D. x = 7, y = 18
Substituting the values, we get:
18/6 ≠ 12/4 ≠ 21/7
Therefore, D is not the correct answer.
In conclusion, the correct values are x = 14 and y = 18, so the answer is C.
everything on ABC is 12/4 = 3 times the corresponding length on DEF
x = 21/3
y = 3*6