A triangle with unequal sides with the base labelled 6 and height labelled 4.

Question

Mike draws a triangle and dilates it by a scale factor of 2.5. If the triangle’s original dimensions are 4 inches high and 6 inches along its base, what is the area in square inches of Mike’s dilated triangle?

(1 point)
Responses

150
150

75
75

60
60

24

Answer 1

The area of a triangle can be calculated using the formula A = (base * height) / 2.

For the original triangle, the base is 6 inches and the height is 4 inches:
A_original = (6 * 4) / 2 = 12 square inches.

When the triangle is dilated by a scale factor of 2.5, both the base and height will also be multiplied by 2.5.

The new base will be 6 * 2.5 = 15 inches.
The new height will be 4 * 2.5 = 10 inches.

The area of Mike's dilated triangle is calculated as:
A_dilated = (15 * 10) / 2 = 150 square inches.

Therefore, the area in square inches of Mike's dilated triangle is 150.