Question

EASY GEOMETRY!!!!!

PLS HELP!!!!!!!!!
Figure A has an area of 36 meters squared, while Figure B has an area of 81 meters squared.
What is the scale factor of the perimeter from Figure A to Figure B?



If Figure A has a side length of 3 meters, what must be the length of the corresponding side in Figure B?
meters

Answer 1

(a) Let the scale factor of the perimeter from Figure A to Figure B be denoted by k. The ratio of the perimeters of two similar figures is equal to the scale factor of the corresponding lengths.

Since the area of Figure A is 36 square meters and its side length is 3 meters, we can calculate its perimeter as:

Perimeter of Figure A = 4 × 3 = 12 meters

Similarly, since the area of Figure B is 81 square meters, we can calculate its side length as:

Side length of Figure B = √(81) = 9 meters

Therefore, the perimeter of Figure B is:

Perimeter of Figure B = 4 × 9 = 36 meters

Now we can use the ratio of the perimeters to find the scale factor:

k = Perimeter of Figure B / Perimeter of Figure A

k = 36 / 12

k = 3

Therefore, the scale factor of the perimeter from Figure A to Figure B is 3.

(b) Since the scale factor of the lengths from Figure A to Figure B is also 3 (because the area scale factor is the square of the length scale factor), we can find the length of the corresponding side in Figure B by multiplying the length of the corresponding side in Figure A by 3.

If the side length of Figure A is 3 meters, then the length of the corresponding side in Figure B is:

Length of corresponding side in Figure B = 3 × 3

Length of corresponding side in Figure B = 9 meters

Therefore, the length of the corresponding side in Figure B is 9 meters.