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 75 75 60 60 24 24 150 150
Answers
GPT-4o mini
To find the area of Mike's dilated triangle, we first calculate the area of the original triangle using the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
The original triangle has a height of 4 inches and a base of 6 inches. Therefore, the area of the original triangle is:
\[
\text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches}
\]
Since the triangle is dilated by a scale factor of 2.5, the dimensions of the triangle after dilation will be multiplied by this scale factor. The new dimensions are:
- Height: \(4 \times 2.5 = 10\) inches
- Base: \(6 \times 2.5 = 15\) inches
Now, we calculate the area of the dilated triangle using the same area formula:
\[
\text{Area}_{\text{dilated}} = \frac{1}{2} \times \text{base}_{\text{dilated}} \times \text{height}_{\text{dilated}} = \frac{1}{2} \times 15 \times 10
\]
Calculating this gives:
\[
\text{Area}_{\text{dilated}} = \frac{1}{2} \times 150 = 75 \text{ square inches}
\]
Thus, the area of Mike's dilated triangle is **75 square inches**.
The correct response is: **75**.
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
The original triangle has a height of 4 inches and a base of 6 inches. Therefore, the area of the original triangle is:
\[
\text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches}
\]
Since the triangle is dilated by a scale factor of 2.5, the dimensions of the triangle after dilation will be multiplied by this scale factor. The new dimensions are:
- Height: \(4 \times 2.5 = 10\) inches
- Base: \(6 \times 2.5 = 15\) inches
Now, we calculate the area of the dilated triangle using the same area formula:
\[
\text{Area}_{\text{dilated}} = \frac{1}{2} \times \text{base}_{\text{dilated}} \times \text{height}_{\text{dilated}} = \frac{1}{2} \times 15 \times 10
\]
Calculating this gives:
\[
\text{Area}_{\text{dilated}} = \frac{1}{2} \times 150 = 75 \text{ square inches}
\]
Thus, the area of Mike's dilated triangle is **75 square inches**.
The correct response is: **75**.