Question

the right triangle below is dilated by a scale factor of \\( \frac { 1 } { 5 } \\). 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
area of given right triangle \\( \square \\) units \\( ^ { 2 } \\)
perimeter of dilated right triangle \\( \square \\) units
area of dilated right triangle \\( \square \\) units \\( ^ { 2 } \\)
answer attempt 1 out of 2

Explanation:

Step1: Calculate perimeter of original triangle

Perimeter formula for triangle \(P=a + b + c\). Here \(a = 80\), \(b=60\), \(c = 100\).
\(P_{original}=80 + 60+100=240\)

Step2: Calculate area of original triangle

Area formula for right - triangle \(A=\frac{1}{2}\times base\times height\). Here base \(=80\), height \(=60\).
\(A_{original}=\frac{1}{2}\times80\times60 = 2400\)

Step3: Calculate perimeter of dilated triangle

When a figure is dilated by a scale factor \(k=\frac{1}{5}\), the perimeter of the dilated figure \(P_{dilated}=k\times P_{original}\)
\(P_{dilated}=\frac{1}{5}\times240 = 48\)

Step4: Calculate area of dilated triangle

When a figure is dilated by a scale factor \(k=\frac{1}{5}\), the area of the dilated figure \(A_{dilated}=k^{2}\times A_{original}\)
\(A_{dilated}=(\frac{1}{5})^{2}\times2400=\frac{1}{25}\times2400 = 96\)

Answer:

Perimeter of given right triangle: \(240\) units
Area of given right triangle: \(2400\) units²
Perimeter of dilated right triangle: \(48\) units
Area of dilated right triangle: \(96\) units²