Question

triangle mno is dilated by a scale factor of 2.5 to form △mno. perimeter △mno = 22.5 m. area △mno = 9.8 m². perimeter △mno. area △mno. 3. dilate each figure or answer the question using the information provided. then, compare and contrast the corresponding angles and side lengths of the original figure and dilated figure. in each, compare the area of the original figure to the area or

Explanation:

Step1: Recall the scale - factor rules for perimeter and area

When a figure is dilated by a scale factor \(k\), the perimeter of the dilated figure is related to the perimeter of the original figure by \(P'=kP\), and the area of the dilated figure is related to the area of the original figure by \(A' = k^{2}A\). Here, \(k = 2.5\).

Step2: Calculate the perimeter of \(\triangle M'N'O'\)

Given the perimeter of \(\triangle MNO=22.5\) m. Using the formula \(P'=kP\), substitute \(k = 2.5\) and \(P = 22.5\) m. So \(P'=2.5\times22.5=56.25\) m.

Step3: Calculate the area of \(\triangle M'N'O'\)

Given the area of \(\triangle MNO = 9.8\) m². Using the formula \(A'=k^{2}A\), substitute \(k = 2.5\) and \(A = 9.8\) m². First, \(k^{2}=2.5^{2}=6.25\). Then \(A'=6.25\times9.8 = 61.25\) m².

Answer:

Perimeter of \(\triangle M'N'O'=56.25\) m
Area of \(\triangle M'N'O'=61.25\) m²