Question

Use the image to answer the question.

A triangle is bisected by a vertical line that extends from its vertex to its base. The number 6 is marked near the center of the vertical line. The number 4 is marked near where the vertical line intersects the base of the triangle.

Marisol draws a triangle with a 4-inch base and 6-inch height. She dilates the triangle by a scale factor of 1.5. Compare the areas of the dilated triangle and the original triangle. Use a decimal response if necessary.

(1 point)
The area of the dilated triangle is
times the area of the original triangle.

Answer 1

2.25

Reason: area scales by the square of the linear scale factor (1.5^2 = 2.25). For example, original area = 0.5·4·6 = 12; dilated area = 0.5·(1.5·4)·(1.5·6) = 27; 27/12 = 2.25.