Question

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. 60 32 68 answer attempt 1 out of 5 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: Calculate perimeter of given triangle

Add side - lengths: $60 + 32+68=160$

Step2: Calculate perimeter of dilated triangle

Multiply perimeter of given triangle by scale - factor. $160\times\frac{1}{4}=40$

Step3: Calculate area of given triangle

Use formula $A=\frac{1}{2}bh$. Here $b = 60$ and $h = 32$, so $A=\frac{1}{2}\times60\times32=960$

Step4: Calculate area of dilated triangle

Multiply area of given triangle by the square of the scale - factor. $960\times(\frac{1}{4})^2=960\times\frac{1}{16}=60$

Answer:

Perimeter of given right triangle: $160$ units
Perimeter of dilated right triangle: $40$ units
Area of given right triangle: $960$ units²
Area of dilated right triangle: $60$ units²