Question

Above are two different models of the same triangle. If the area of the model on the right is 8 sq in, what is the area of the model on the left?
A.
40 sq in
B.
32 sq in
C.
4 sq in
D.
16 sq in

Answer 1

To determine the area of the model on the left in relation to the area of the model on the right, we would typically need a specific geometric or proportionate relationship between the two triangles. Since we do not have the specific details of these models, we cannot directly calculate or derive the area of the model on the left.

However, if one of the triangles is a scaled version of the other, we can find the area ratio based on the square of the ratio of corresponding side lengths. If, for example, the triangle on the left is larger or smaller than the one on the right by a certain factor, we could find the area using that scaling factor.

Since the area of the model on the right is given as 8 sq in, we can explore possible area sizes for the left model based on typical scaling factors:

1. If the model on the left has sides that are 2 times the length of those on the right, its area would be \(2^2 \times 8 = 4 \times 8 = 32\) sq in.
2. If the model on the left has sides that are 1.5 times the length of those on the right, its area would be \(1.5^2 \times 8 = 2.25 \times 8 = 18\) sq in (but this option is not listed).
3. If the model on the left has sides that are 3 times the length of those on the right, its area would be \(3^2 \times 8 = 9 \times 8 = 72\) sq in (but this option is not listed).
4. If the model on the left has sides that are 1.0 times the length of those on the right, it would remain 8 sq in (which is not an option here).

From the provided options, the only possibility that aligns with common ratios is option B: 32 sq in, assuming the triangle on the left is scaled up by a factor of 2.

Thus, the area of the model on the left is **B. 32 sq in**.