Question

The figures are similar. Find the missing corresponding side length.



Figure A has an area of 48 square feet and one of the side lengths is 6 feet. Figure B has an area of 75 square feet.

Answer 1

The answer to this problem is at the end of this message, please read through this to make sure you understand all of the concepts.

To find the missing corresponding side length, we need to use the concept of similarity between the two figures.
Since Figure A and Figure B are similar, their corresponding side lengths are proportional.
Let's say the missing corresponding side length in Figure B is x.
The ratio of the corresponding side lengths between the two figures is:
(side length of Figure B) / (side length of Figure A) = x / 6

The ratio of their areas is also equal to the square of the ratio of their corresponding side lengths:

(area of Figure B) / (area of Figure A) = (x / 6)^2 = 75 / 48
Simplifying the equation yields:
x^2 / 36 = 75 / 48

Cross-multiplying gives:
48x^2 = 36 * 75

Dividing both sides by 48:
x^2 = (36 * 75) / 48
x^2 = 56.25

Taking the square root of both sides:
x = √56.25
x ≈ 7.5

Therefore, the missing corresponding side length in Figure B is approximately 7.5 feet.