leg 7, hypotenuse 25, leg 24

Question

Suppose the triangle in the diagram is dilated by a scale factor of 14
. What is the perimeter of the dilated triangle?

Answer 1

To find the perimeter of the dilated triangle, we first calculate the perimeter of the original triangle.

The lengths of the legs are given as 7 and 24, and the hypotenuse is given as 25. Let's calculate the perimeter of the triangle:

\[ \text{Perimeter} = \text{Leg 1} + \text{Leg 2} + \text{Hypotenuse} = 7 + 24 + 25 \]

Calculating this gives us:

\[ \text{Perimeter} = 7 + 24 + 25 = 56 \]

Next, since the triangle is dilated by a scale factor of 14, we multiply the perimeter of the original triangle by the scale factor:

\[ \text{Perimeter of dilated triangle} = \text{Original Perimeter} \times \text{Scale Factor} = 56 \times 14 \]

Calculating this gives:

\[ \text{Perimeter of dilated triangle} = 56 \times 14 = 784 \]

Thus, the perimeter of the dilated triangle is \( \boxed{784} \).

Answer 2

the dialation is 1/4

Answer 3

If the dilation scale factor is \( \frac{1}{4} \), we can find the perimeter of the dilated triangle by first recalling the perimeter of the original triangle, which we calculated to be 56.

To find the perimeter of the dilated triangle, we multiply the original perimeter by the scale factor of \( \frac{1}{4} \):

\[ \text{Perimeter of dilated triangle} = \text{Original Perimeter} \times \text{Scale Factor} = 56 \times \frac{1}{4} \]

Calculating this gives:

\[ \text{Perimeter of dilated triangle} = 56 \times \frac{1}{4} = 14 \]

Thus, the perimeter of the dilated triangle is \( \boxed{14} \).