Question

Figures A and b are similar. Figure A has an area of 18 square feet. Figure b has an area of 98 square feet and one of the sides lengths is 14 feet find the corresponding side length

Answer 1

To find the corresponding side length of figure B, set up a proportion using the known side length and area of figure B and the unknown side length of figure A. Solve for the side length of A using the proportion. The corresponding side length of figure A is approximately 5.09 feet.

Step-by-step explanation:

To find the corresponding side length of figure B, we can use the concept of similarity. Since figures A and B are similar, their corresponding side lengths are proportional. We can set up a proportion using the known side length of figure B (14 feet) and its area (98 square feet) and the unknown side length of figure A:

(side length of A) / (side length of B) = √(area of A / area of B)

Substituting the given values:

(side length of A) / 14 = √(18 / 98)

Solving for the side length of A:

side length of A = 14 * √(18 / 98)

Therefore, the corresponding side length of figure A is approximately 5.09 feet.

Answer 2

6 ft

Step-by-step explanation:

The ratio of the square of the sides of two similar figures = the ratio of their area

Let x represent the missing side corresponding side length

Therefore,

Area of figure B/area of figure A = square of side length of figure B/square of the side length of figure A

Thus:

98/18 = 14²/x²

98/18 = 196/x²

Cross multiply

98*x² = 196*18

98x² = 3,528

Divide both sides by 98

x² = 3,528/98

x² = 36

x = √36

x = 6

Therefore, missing corresponding side length = 6 ft