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 id the perimeter of Quadrilateral B?

Answer 1

The perimeter of Quadrilateral B is 12 units.

Explanation:

Since Quadrilateral B is a scaled copy of Quadrilateral A, all B's corresponding sides are proportional to A's corresponding sides. This means that the ratio of corresponding sides in A and B will be the same.

Let's find the ratio of corresponding sides between Quadrilateral A and Quadrilateral B using their shortest sides:

Ratio = Shortest side of B / Shortest side of A

Ratio = 2 / 6

Ratio = 1/3

Now, apply this ratio to the other sides of Quadrilateral A to find the sides of Quadrilateral B:

Side 1 of B = Side 1 of A * Ratio = 9 * (1/3) = 3

Side 2 of B = Side 2 of A * Ratio = 9 * (1/3) = 3

Side 3 of B = Side 3 of A * Ratio = 12 * (1/3) = 4

The last side of Quadrilateral B is already given as 2.

Now, add up the sides of Quadrilateral B to find its perimeter:

Perimeter of B = Side 1 + Side 2 + Side 3 + Side 4

Perimeter of B = 3 + 3 + 4 + 2 = 12

Therefore, the perimeter of Quadrilateral B is 12 units.