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 60 60 150 150 75 75 24

Answer 1

To find the area of Mike's dilated triangle, we first need to calculate the area of the original triangle and then apply the scale factor.

1. Calculate the area of the original triangle: The area \( A \) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] For the original triangle, the base is 6 inches and the height is 4 inches: \[ A = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches} \]

2. Determine the area of the dilated triangle: When a triangle is dilated by a scale factor \( k \), the area of the dilated triangle changes by the square of the scale factor: \[ \text{Area of dilated triangle} = k^2 \times \text{Area of original triangle} \] In this case, the scale factor \( k = 2.5 \): \[ \text{Area of dilated triangle} = (2.5)^2 \times 12 \] Calculate \( (2.5)^2 \): \[ (2.5)^2 = 6.25 \]

   Now, calculate the area: \[ \text{Area of dilated triangle} = 6.25 \times 12 = 75 \text{ square inches} \]

So the area of Mike’s dilated triangle is 75 square inches.