Question

Saquina dilates a digital photograph by a factor of 1.75 to create a new digital photograph similar to her original photograph. Select from the drop-menus to correctly complete the statement. The perimeter of Saquina's new photograph is times larger than the perimeter of her original photograph, and the area of her new photograph is times larger than the area of her original photograph.

Answer 1

1: 1.75

2: 3.0625

Explanation:

I took the test

Answer 2

Perimeter = 1.75 times larger

Area = 3.0625 times larger

Explanation:

Let the original quadrilateral have sides of a, b, c, d

Perimeter of the New Photograph

• Then the perimeter of the original is P = (a + b + c + d)
• Now the perimeter of the new quad is P = 1.75a + 1.75b + 1.75c + 1.75d
• Using the distributive Property we get P = 1.75(a + b + c + d) So the new perimeter is 1.75*the old perimeter.

Area of the New Photograph

The area is a little harder. Suppose the Old figure had an Area found by the formula of

• Area = e * f Each measurement is increased by a factor of 1.75
• Area_new = 1.75e * 1.75f
• Area_new = 3.0625 * e * f
• Area_new = 3.0625 * old area