Suppose the triangle in a diagram was dilated using a scale factor of 2. What is the perimeter of the dilated triangle?

Question

one leg is 24 cm
one leg is 7 cm
the hypotenuse is 25 cm

Answer 1

To find the perimeter of the dilated triangle, we first need to calculate the perimeter of the original triangle and then use the scale factor to find the perimeter of the dilated triangle.

1. Calculate the perimeter of the original triangle: The original triangle has legs of lengths 24 cm and 7 cm, and a hypotenuse of 25 cm. The perimeter \( P \) of the triangle is the sum of the lengths of its sides:

   \[ P = 24 , \text{cm} + 7 , \text{cm} + 25 , \text{cm} = 56 , \text{cm} \]

2. Apply the scale factor of 2: When a triangle is dilated by a scale factor of \( k \), the perimeter of the dilated triangle is \( k \) times the perimeter of the original triangle. In this case, the scale factor \( k \) is 2.

   \[ \text{Perimeter of dilated triangle} = k \times P = 2 \times 56 , \text{cm} = 112 , \text{cm} \]

Therefore, the perimeter of the dilated triangle is 112 cm.