Questions: The right triangle below is dilated by a scale factor of 2. 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. Perimeter of given right triangle □ units Perimeter of dilated right triangle □ units Area of given right triangle □ units ^2 Area of dilated right triangle □ units ^2

$The right triangle below is dilated by a scale factor of 2. Find the perimeter and area of the right triangle below, as well as the perimeter and area of the dilated right triangle. Express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). Figures are not necessarily drawn to scale. Perimeter of given right triangle □ units Perimeter of dilated right triangle □ units Area of given right triangle □ units ^2 Area of dilated right triangle □ units ^2$

Transcript text: The right triangle below is dilated by a scale factor of 2. 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. Perimeter of given right triangle $\square$ units Perimeter of dilated right triangle $\square$ units Area of given right triangle $\square$ units $^{2}$ Area of dilated right triangle $\square$ units $^{2}$

Solution

Solution Steps

Step 1: Calculate the Perimeter of the Given Right Triangle

The given right triangle has sides of lengths 24, 10, and 26 units. The perimeter is the sum of the lengths of all sides. \[ \text{Perimeter} = 24 + 10 + 26 = 60 \text{ units} \]

Step 2: Calculate the Area of the Given Right Triangle

The area of a right triangle is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Here, the base is 24 units and the height is 10 units. \[ \text{Area} = \frac{1}{2} \times 24 \times 10 = 120 \text{ units}^2 \]

Step 3: Calculate the Perimeter of the Dilated Right Triangle

The triangle is dilated by a scale factor of 2. The new side lengths are: \[ 24 \times 2 = 48 \text{ units} \] \[ 10 \times 2 = 20 \text{ units} \] \[ 26 \times 2 = 52 \text{ units} \] The perimeter of the dilated triangle is: \[ \text{Perimeter} = 48 + 20 + 52 = 120 \text{ units} \]