Question

the right triangle below is dilated by a scale factor of $\frac{1}{2}$. 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.
answer attempt 1 out of 2
perimeter of given right triangle units
area of given right triangle units²
perimeter of dilated right triangle units
area of dilated right triangle units²

Explanation:

Step1: Calculate perimeter of given triangle

Perimeter of a triangle is sum of its sides.
$$30 + 72+78=180$$

Step2: Calculate area of given triangle

Area of a right - triangle is $\frac{1}{2}\times base\times height$.
$$\frac{1}{2}\times30\times72 = 1080$$

Step3: Calculate perimeter of dilated triangle

When a figure is dilated by a scale factor $k$, its perimeter is also dilated by $k$. Here $k = \frac{1}{2}$.
$$180\times\frac{1}{2}=90$$

Step4: Calculate area of dilated triangle

When a figure is dilated by a scale factor $k$, its area is dilated by $k^{2}$. Here $k=\frac{1}{2}$.
$$1080\times(\frac{1}{2})^{2}=1080\times\frac{1}{4} = 270$$

Answer:

Perimeter of given right triangle: $180$ units
Area of given right triangle: $1080$ units²
Perimeter of dilated right triangle: $90$ units
Area of dilated right triangle: $270$ units²