Answer:
Step-by-step explanation:
For the first one it looks like you are just going to have to measure sides and angles and then draw shapes that have the same angle measures, but however longer or shorter it tells you. So for the right triangle A it says a scale factor of 2 so each side length is going to be double what the original is, shape B will be redrawn with half the lengths and shape C will be redrawn with the lengths multiplied by 3/2, or 1.5. Again though, angle measures stay the same.
2 thankfully doesn't involve measuring. it's important to know that if you scale a shape it doesn't change the relationship of the sides. So the longest will be the longest after being scaled, the shortest will be the shortest and even the leftmost side will always be the leftmost side unless other transformations are carried out, like rotations or something. Though even with rotations, shortest will always be the shortest and so on.
Anyway, perimeter is the sum of the side lengths. Of shape A that is 6+9+9+12 = 36. Now we want the perimeter for shape B. It doesn't directly give us the measures, but it does tell us it s scaled so the shortest side from shape A is now 2. Well what side was the shortest on shape A? 6 was, so we know that the scaling factor is 1/3 since 6*1/3 = 2. That means all the other sides get the same scaling factor. so 9*1/3 and 12/3 which are 3 and 4 respectively. Now we know the side lengths are 2.3,3 and 4 and the perimeter is 12. Also, I want to point out the relationship between the two perimeters. what do you multiply 36 by to get to 12? 1/3, so the same thinking applies to sides as it does perimeter. So if you know the scaling factor you can just multiply the perimeter by it to find the new perimeter. Which is going to come in handy for the next question.
3 we can find the scaling factor y seeing what we multiply the original perimeter by to get 30, then we can just apply that to the different sides. Well, the side lengths of the original shape are 3, 1, 2, 1, and 2. So that makes the perimeter 9. Now, what do we multiply 9 by to get 30? It's not a nice number but if you solve an algebraic expression 9x=30 you get 30/9 or 10/3, or if you'd rather a mixed number it's 3 and 1/3. I am going to stick with 10/3. Now, if you multiply the sides we started with by 10/3 you get 3*(10/3)=10, 1*(10/3)=10/3 and 2*(10/3)=20/3. So the sides as I listed them before are 10, 10/3, 20/3, 10/3 and 20/3. If you add them up you get 10+ 10/3 + 20/3 + 10/3 + 10/3. Adding up the fractions is easy since they share a denominator, it becomes 60/3 or 20. Then it's just 20+10 which is 30, so it does give us the perimeter we want.
If there was anything you didn't understand let me know.
