Question

the right triangle below is dilated by a scale factor of 5. find the perimeter and area of the right triangle below, as well as the perimeter and area of the dilated right triangle. express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). figures are not necessarily drawn to scale.
answer attempt 1 out of 2
perimeter of given right triangle
units
perimeter of dilated right triangle
units
area of given right triangle
units²
area of dilated right triangle
units²

Explanation:

Step1: Find perimeter of given triangle

The sides of the given right triangle are 8, 15, and 17. Perimeter is the sum of all sides. So, we calculate \( 8 + 15 + 17 \).
\( 8 + 15 + 17 = 40 \)

Step2: Find area of given triangle

For a right triangle, area is \( \frac{1}{2} \times \text{base} \times \text{height} \). Here, base = 15 and height = 8 (or vice versa). So, \( \frac{1}{2} \times 15 \times 8 \).
\( \frac{1}{2} \times 15 \times 8 = 60 \)

Step3: Find perimeter of dilated triangle

When a figure is dilated by a scale factor \( k \), the perimeter is scaled by \( k \). The scale factor here is 5. So, perimeter of dilated triangle is \( 40 \times 5 \).
\( 40 \times 5 = 200 \)

Step4: Find area of dilated triangle

When a figure is dilated by a scale factor \( k \), the area is scaled by \( k^2 \). So, area of dilated triangle is \( 60 \times 5^2 \).
\( 60 \times 25 = 1500 \)

Answer:

Perimeter of given right triangle: 40 units
Perimeter of dilated right triangle: 200 units
Area of given right triangle: 60 units²
Area of dilated right triangle: 1500 units²