Question

the right triangle below is dilated by a scale factor of 3. 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

Perimeter is sum of all sides. Sides are 7, 24, 25.
$Perimeter_{given} = 7 + 24 + 25$
$= 56$

Step2: Find area of given triangle

Area of right triangle is $\frac{1}{2} \times base \times height$. Base = 24, height = 7.
$Area_{given} = \frac{1}{2} \times 24 \times 7$
$= 12 \times 7 = 84$

Step3: Find perimeter of dilated triangle

Dilation scale factor 3. Perimeter scales by scale factor.
$Perimeter_{dilated} = Perimeter_{given} \times 3$
$= 56 \times 3 = 168$

Step4: Find area of dilated triangle

Area scales by square of scale factor.
$Area_{dilated} = Area_{given} \times 3^2$
$= 84 \times 9 = 756$

Answer:

Perimeter of given right triangle: 56 units
Perimeter of dilated right triangle: 168 units
Area of given right triangle: 84 units²
Area of dilated right triangle: 756 units²