Let's go through each question one by one:
Question 1
A) A triangle has side lengths of 2, 6, and 7 units, and a similar but larger triangle has corresponding side lengths of 6, 18, and 21 units. Calculate and compare the perimeters of the triangles. What is the ratio of the corresponding sides of the smaller triangle to the larger triangle?
- Perimeter of smaller triangle: \(2 + 6 + 7 = 15\) units
- Perimeter of larger triangle: \(6 + 18 + 21 = 45\) units
- The ratio of the smaller triangle to the larger triangle sides: \[ \text{Ratio} = \frac{2}{6} = \frac{1}{3} \]
The correct answer is: Start Fraction 1 over 3 End Fraction
Question 2
A) In the diagram, the smaller square has side lengths of 13 centimeters, and the larger square has side lengths of 39 centimeters. Calculate and compare the perimeters. What is the ratio of the perimeter of the larger square to the smaller square?
- Perimeter of smaller square: \(4 \times 13 = 52\) cm
- Perimeter of larger square: \(4 \times 39 = 156\) cm
- The ratio of the larger perimeter to the smaller perimeter: \[ \text{Ratio} = \frac{156}{52} = 3 \]
The correct answer is: Start Fraction 3 over 1 End Fraction
Question 3
A) A trapezoid has a base of 10 inches, sides of 8 inches, and a top length of 4 inches. Suppose the trapezoid is dilated using a scale factor of 12. What is the perimeter of the dilated trapezoid?
- Original perimeter: \(10 + 8 + 8 + 4 = 30\) inches
- Dilation by scale factor of 12: \[ \text{Perimeter of dilated trapezoid} = 30 \times 12 = 360 \text{ inches} \]
However, none of the options match \(360\) inches (assuming the problem has correct numbers).
Since the provided options may be examples rather than the final response to the perimeter, please recheck this detail or let me know if there's an error in transmission.
Question 4
A) Ross draws a triangle with side lengths of 6, 6, and 5 cm. Suppose he plans to draw the same triangle dilated with a scale factor of 4. What is the perimeter of the dilated triangle?
- Original perimeter: \(6 + 6 + 5 = 17\) cm
- Dilation by scale factor of 4: \[ \text{Perimeter of dilated triangle} = 17 \times 4 = 68 \text{ cm} \]
The correct answer is: 68 cm
Question 5
A) Suppose the triangle in the diagram was dilated using a scale factor of 2. What is the perimeter of the dilated triangle?
- Original sides: \(24\) cm (base), \(7\) cm (height), \(25\) cm (hypotenuse)
- Original perimeter: \(24 + 7 + 25 = 56\) cm
- Dilation by scale factor of 2: \[ \text{Perimeter of dilated triangle} = 56 \times 2 = 112 \text{ cm} \]
Again, ensure the problem and options provided are aligned, as they may not match the computed perimeter.
If there are any discrepancies or further questions, please let me know!