Question

If the ratio of the lengths of corresponding sides of two similar triangles is 2 : 3, and the area of the smaller triangle is 36 in^2, what is the area of the larger triangle?

A. 24 in.^2
B. 54 in.^2
C. 81 in.^2
D. 90 in.^2
Even tho I don't need to explain my answer please do cuz I'm having a hard time understanding this

Answer 1

To find the area of the larger triangle with a given scale factor and area of the smaller triangle, use the formula: area of larger triangle = (scale factor)^2 × area of smaller triangle.

Step-by-step explanation:

To find the area of the larger triangle, we need to determine the scale factor between the two similar triangles. Given that the ratio of the lengths of corresponding sides is 2:3, we can say that the scale factor is 3/2, since the lengths of the corresponding sides are multiplied by this factor to get to the larger triangle.

Now, recall that the area of a triangle is given by the formula: Area = 1/2 × base × height. Since the scale factor is 3/2, the area of the larger triangle will be (3/2)^2 = 9/4 times the area of the smaller triangle.

Therefore, the area of the larger triangle is (9/4) × 36 in^2 = 81 in^2. The correct answer is C. 81 in^2.