Question

A right triangle has a base of 5 ft and a height of 12 ft. A similar triangle has an area of 270 square feet. What are the dimensions of the similar triangle?

a) Base = 15 ft, Height = 36 ft
b) Base = 9 ft, Height = 27 ft
c) Base = 10 ft, Height = 30 ft
d) Base = 18 ft, Height = 54 f

Answer 1

a) Base = 15 ft, Height = 36 ft. The dimensions of the similar triangle are base = 15 ft and height = 36 ft.

Step-by-step explanation:

To find the dimensions of the similar triangle, we need to calculate the scale factor between the two triangles. The scale factor can be found by taking the square root of the ratio of the areas of the two triangles. In this case, the area of the original triangle is (1/2) * 5 * 12 = 30 square feet. The scale factor is then sqrt(270/30) = sqrt(9) = 3. Therefore, the dimensions of the similar triangle are the original dimensions multiplied by the scale factor. The base of the similar triangle is 5 * 3 = 15 ft and the height is 12 * 3 = 36 ft. So, the answer is option a) Base = 15 ft, Height = 36 ft.