Pergunta
![Question 11
Figures A and B are similar.
Figure A has an area of 48ft^2 and one side of 6 ft.
Figure B has an area of 75ft^2
The corresponding side length of Figure B is __ (your answer is a decimal)
Blank 1: square](https://static.questionai.br.com/resource%2Fqaiseoimg%2F202501%2Fquestion-11figures-b-similarfigure-area-48ft2-one-side-6-tmZK9J5xSs05.jpg?x-oss-process=image/resize,w_558,h_500/quality,q_35/format,webp)
Question 11 Figures A and B are similar. Figure A has an area of 48ft^2 and one side of 6 ft. Figure B has an area of 75ft^2 The corresponding side length of Figure B is __ (your answer is a decimal) Blank 1: square
Solução
![expert verified](https://mathresource.studyquicks.com/static/image/br/verify.png)
4.5372 Voting
![avatar](https://static.questionai.br.com/resource%2Favatar%2Fbr%2Fmale%2Fa1597_96ab60e04bfac60530dd.jpg?x-oss-process=image/format,webp)
ValdirMestre · Tutor por 5 anos
Responder
To solve this problem, we need to find the corresponding side length of Figure B.
Given information:
- Figures A and B are similar.
- Figure A has an area of 48 ft² and one side of 6 ft.
- Figure B has an area of 75 ft².
Step 1: Find the scale factor between the two figures.
Since the figures are similar, the ratio of their corresponding side lengths is equal to the square root of the ratio of their areas.
Scale factor = √(Area of Figure B / Area of Figure A)
Scale factor = √(75 ft² / 48 ft²)
Scale factor = √(1.5625)
Scale factor = 1.25
Step 2: Find the corresponding side length of Figure B.
Since the figures are similar, the corresponding side length of Figure B can be found by multiplying the side length of Figure A by the scale factor.
Corresponding side length of Figure B = Side length of Figure A × Scale factor
Corresponding side length of Figure B = 6 ft × 1.25
Corresponding side length of Figure B = 7.5 ft
Therefore, the corresponding side length of Figure B is 7.5 ft.
Given information:
- Figures A and B are similar.
- Figure A has an area of 48 ft² and one side of 6 ft.
- Figure B has an area of 75 ft².
Step 1: Find the scale factor between the two figures.
Since the figures are similar, the ratio of their corresponding side lengths is equal to the square root of the ratio of their areas.
Scale factor = √(Area of Figure B / Area of Figure A)
Scale factor = √(75 ft² / 48 ft²)
Scale factor = √(1.5625)
Scale factor = 1.25
Step 2: Find the corresponding side length of Figure B.
Since the figures are similar, the corresponding side length of Figure B can be found by multiplying the side length of Figure A by the scale factor.
Corresponding side length of Figure B = Side length of Figure A × Scale factor
Corresponding side length of Figure B = 6 ft × 1.25
Corresponding side length of Figure B = 7.5 ft
Therefore, the corresponding side length of Figure B is 7.5 ft.
Clique para avaliar: