Question
If you want to dilate an isosceles right triangle with a hypotenuse of 18 yards to create a dilated image with a hypotenuse of 12 yards, what scale factor should you use?
a. 3/2
b. 2/3 yards
c. 6 yards
d. 2/3
a. 3/2
b. 2/3 yards
c. 6 yards
d. 2/3
Answers
GPT-4o mini
To find the scale factor for dilating the isosceles right triangle, we can use the formula for the scale factor, which is the ratio of the lengths of the corresponding sides of the original triangle and the dilated image.
Given:
- Original hypotenuse = 18 yards
- Dilated hypotenuse = 12 yards
The scale factor (k) can be calculated as follows:
\[
k = \frac{\text{Dilated hypotenuse}}{\text{Original hypotenuse}} = \frac{12 \text{ yards}}{18 \text{ yards}} = \frac{12}{18} = \frac{2}{3}
\]
Thus, the correct scale factor to use for the dilation is \( \frac{2}{3} \).
The answer is:
d. \( \frac{2}{3} \)
Given:
- Original hypotenuse = 18 yards
- Dilated hypotenuse = 12 yards
The scale factor (k) can be calculated as follows:
\[
k = \frac{\text{Dilated hypotenuse}}{\text{Original hypotenuse}} = \frac{12 \text{ yards}}{18 \text{ yards}} = \frac{12}{18} = \frac{2}{3}
\]
Thus, the correct scale factor to use for the dilation is \( \frac{2}{3} \).
The answer is:
d. \( \frac{2}{3} \)