Question

Quadrilateral A has side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 2. What is the perimeter of Quadrilateral B?

a. 6
b. 9
c. 12
d. 18

Answer 1

By finding the scale factor of 1/3 and multiplying the side lengths of Quadrilateral A by it, we determine that Quadrilateral B has a perimeter of 12.

Step-by-step explanation:

The question asks for the perimeter of a scaled copy of Quadrilateral A, which has side lengths of 6, 9, 9, and 12, such that its shortest side in Quadrilateral B is of length 2. To solve this, we can first find the scale factor by dividing the shortest side of Quadrilateral B by the shortest side of Quadrilateral A (2 ÷ 6 = 1/3). This means that all sides of Quadrilateral B are 1/3 the length of Quadrilateral A's sides.

Therefore, we multiply each side of Quadrilateral A by 1/3 to get the sides of Quadrilateral B:

• 6 × 1/3 = 2
• 9 × 1/3 = 3
• 9 × 1/3 = 3
• 12 × 1/3 = 4

Adding all these sides together gives us the perimeter of Quadrilateral B:

Perimeter = 2 + 3 + 3 + 4 = 12.

So, the correct answer is (c) 12.