Questions: The right triangle below is dilated by a scale factor of 1/4. 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.

$The right triangle below is dilated by a scale factor of 1/4. Find the perimeter and area of the right triangle below, as well as the perimeter and area of the dilated right triangle. Express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). Figures are not necessarily drawn to scale.$

Transcript text: The right triangle below is dilated by a scale factor of $\frac{1}{4}$. 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.

Solution

Solution Steps

Step 1: Find the perimeter of the original triangle

The perimeter of a triangle is the sum of its sides. In this case, the sides are 18, 24, and 30. Perimeter = 18 + 24 + 30 = 72

Step 2: Find the area of the original triangle

The area of a right triangle is given by (1/2) * base * height. Here, the base is 18 and the height is 24. Area = (1/2) * 18 * 24 = 216

Step 3: Find dimensions of the dilated triangle

The scale factor is 1/4. Multiply each side of the original triangle by 1/4 to find the dimensions of the dilated triangle. Dilated side 1 = (1/4) * 18 = 4.5 Dilated side 2 = (1/4) * 24 = 6 Dilated side 3 = (1/4) * 30 = 7.5