Question

scaled figures perimeter and area (l1)
score: 3/4 penalty: 1 off
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 perimeter of dilated right triangle units
area of given right triangle units² area of dilated right triangle units²

Explanation:

Step1: Calculate the perimeter of the given right - triangle

The perimeter \(P\) of a triangle is the sum of its side lengths.
\(P = 25+60 + 65\)
\(P=150\) units

Step2: Calculate the area of the given right - triangle

The area \(A\) of a right - triangle is given by \(\frac{1}{2}\times base\times height\). Here, base \(b = 60\) and height \(h = 25\)
\(A=\frac{1}{2}\times60\times25\)
\(A = 750\) units²

Step3: Calculate the side lengths of the dilated triangle

When a figure is dilated by a scale factor \(k=\frac{1}{2}\), the new side lengths are \(a'=k\times a\), \(b'=k\times b\), \(c'=k\times c\)
The new side lengths are \(25\times\frac{1}{2}=\frac{25}{2}\), \(60\times\frac{1}{2}=30\), \(65\times\frac{1}{2}=\frac{65}{2}\)

Step4: Calculate the perimeter of the dilated right - triangle

\(P'=\frac{25}{2}+30+\frac{65}{2}\)
\(P'=\frac{25 + 65}{2}+30\)
\(P'=\frac{90}{2}+30\)
\(P'=45 + 30=75\) units

Step5: Calculate the area of the dilated right - triangle

The new base \(b'=30\) and new height \(h'=\frac{25}{2}\)
\(A'=\frac{1}{2}\times30\times\frac{25}{2}\)
\(A'=\frac{750}{4}=\frac{375}{2}=187.5\) units²

Answer:

Perimeter of given right triangle: \(150\) units
Area of given right triangle: \(750\) units²
Perimeter of dilated right triangle: \(75\) units
Area of dilated right triangle: \(187.5\) units²