Question

21. Solve for
22. Solve for d.​

Answer 1

Answer: #21: x=9

#22: d=24

Explanation:

the two triangles in #21 are congruent (you can tell by the red angle thing).

So, match up the sides (like CD to RS and BD to TR) to get 15:55, and (3x-6):77.

then change both into fractions, 15/55 and (3x-6)/77 and set them equal to each other.

15/55=(3x-6)/77

Then use the butterfly method to multiply the top of the first fraction to the bottom of the second fraction. ( so 15*77) Do the same thing with the bottom of the first fraction and the top of the second fraction (so 55* (3x-6)) and set those two things equal to each other.

15*77=55*(3x-6)

15*77= 1,155 and 55 distributed into (3x-6)= 165x-330

so you have 1155=165x-330

then add 330 to both sides to get 1485=165x

then divide by 165 to get 9=x.

22 is the same. take the congruent triangles and line them up. 21:28 and 18:d.

change them into fractions: 21/28 and 18/d

cross multiply (using the butterfly method shown above)

21d=28*18

multiply 28*18 to get 504

divide 504 by 21 to get d=24

Answer 2

21. X = 9

22. D = 24

Explanation:

To solve 21 and 22, we use scale factors

In 21- We know that the two triangles are similar, and if we rotate the smaller one, they look the same. If we look at their sides, we can see a scale factor. 15 & 55 share a common factor: 5, and it's in the ratio 3:11. Now, if we do the same with 3x - 6 and 77, we put them in the ratio of (3x - 6):77 or 3:11, so they share a common factor 7. 3 x 7 = 21, so x must be 9

In 22-

If we rotate the bigger triangle to be in the same direction as the smaller, we can see scale factors. 12 and 16 are in the ratio of 3:4, 21 and 28 are in the ratio of 3:4, so 18:D must be in the ratio of 3:4, so d must be 24.

Hope this helps!! <3