Suppose the triangle in the diagram is dilated by a scale factor of 1/4. 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 determine the perimeter of the original triangle and then apply the scale factor.

1. Calculate the perimeter of the original triangle: \[ \text{Perimeter} = \text{leg}_1 + \text{leg}_2 + \text{hypotenuse} \] Substituting the given lengths: \[ \text{Perimeter} = 24 , \text{cm} + 7 , \text{cm} + 25 , \text{cm} = 56 , \text{cm} \]

2. Apply the scale factor of \( \frac{1}{4} \) to find the perimeter of the dilated triangle: \[ \text{Perimeter of dilated triangle} = \text{Perimeter of original triangle} \times \frac{1}{4} \] Substituting the perimeter we calculated: \[ \text{Perimeter of dilated triangle} = 56 , \text{cm} \times \frac{1}{4} = 14 , \text{cm} \]

Therefore, the perimeter of the dilated triangle is 14 cm.