Question

1. figure efgh has a perimeter of 40 cm and an area of 96 cm². it is dilated by a factor of ½ to create figure efgh. what statement about the perimeter (p) and the area (a) of figure efgh is true?

a. p = 10 cm; a = 6 cm²
b. p = 10 cm; a = 24 cm²
c. p = 160 cm; a = 192 cm²
d. p = 160 cm; a = 384 cm²

Explanation:

Step1: Calculate the perimeter of the dilated figure

When a figure is dilated by a scale factor \(k\), the perimeter of the new figure is \(k\) times the perimeter of the original figure.
Given \(k = \frac{1}{4}\) and the original perimeter \(P_{original}=40\space cm\).
The perimeter of the dilated figure \(P = k\times P_{original}=\frac{1}{4}\times40 = 10\space cm\)

Step2: Calculate the area of the dilated figure

When a figure is dilated by a scale factor \(k\), the area of the new figure is \(k^{2}\) times the area of the original figure.
Given \(k=\frac{1}{4}\) and the original area \(A_{original} = 96\space cm^{2}\)
The area of the dilated figure \(A=k^{2}\times A_{original}=(\frac{1}{4})^{2}\times96=\frac{1}{16}\times96 = 6\space cm^{2}\)

Answer:

A. \(P = 10\space cm; A = 6\space cm^{2}\)