Question
suppose a triangle with leg lengths of 7 and 24 and a hypotenuse of 25 was dilated using a scale factor of 2. What is the perimeter of the dilated triangle?
28
56
112
168
28
56
112
168
Answers
GPT-4o mini
To find the perimeter of the dilated triangle, we first calculate the perimeter of the original triangle. Given a right triangle with leg lengths of 7 and 24, and a hypotenuse of 25, we calculate the perimeter as follows:
\[
\text{Perimeter}_{\text{original}} = 7 + 24 + 25 = 56
\]
Next, when the triangle is dilated using a scale factor of 2, all side lengths are multiplied by 2. Thus, the new leg lengths and hypotenuse are:
\[
\text{New leg length 1} = 7 \times 2 = 14
\]
\[
\text{New leg length 2} = 24 \times 2 = 48
\]
\[
\text{New hypotenuse} = 25 \times 2 = 50
\]
Now, we find the perimeter of the dilated triangle:
\[
\text{Perimeter}_{\text{dilated}} = 14 + 48 + 50
\]
Calculating this:
\[
14 + 48 = 62
\]
\[
62 + 50 = 112
\]
Thus, the perimeter of the dilated triangle is \( \boxed{112} \).
\[
\text{Perimeter}_{\text{original}} = 7 + 24 + 25 = 56
\]
Next, when the triangle is dilated using a scale factor of 2, all side lengths are multiplied by 2. Thus, the new leg lengths and hypotenuse are:
\[
\text{New leg length 1} = 7 \times 2 = 14
\]
\[
\text{New leg length 2} = 24 \times 2 = 48
\]
\[
\text{New hypotenuse} = 25 \times 2 = 50
\]
Now, we find the perimeter of the dilated triangle:
\[
\text{Perimeter}_{\text{dilated}} = 14 + 48 + 50
\]
Calculating this:
\[
14 + 48 = 62
\]
\[
62 + 50 = 112
\]
Thus, the perimeter of the dilated triangle is \( \boxed{112} \).