Large triangle (30¢X, 60¢X, and 90¢X), the base is 15 feet. and small triangle (30¢X, 60¢X, and 90¢X)

the above two triangle the ratio of the perimeter of the large triangle to the perimeter of the small triangle is ¡Ô3. Determine the area of the small triangle rounded to the nearest tenth.

The perimeter of triangle B is 2.5 times greater than the perimeter of triangle A.The area of triangle B is how many times greater than the area of triangle A?

To determine the area of the small triangle, we can first find the ratio of the perimeters and then use that ratio to find the ratio of the areas.

Let's denote the side lengths of the small triangle as 30x, 60x, and 90x, where x is a scale factor. The ratio of the perimeters of the large triangle to the small triangle is √3.

So, we can set up the equation:

(30x + 60x + 90x) / (30 + 60 + 90) = √3

Simplifying, we get:

180x / 180 = √3

x = √3

Now, let's calculate the area of the small triangle. The formula for the area of a triangle is:

Area = 1/2 * base * height

We know the base is 15 feet, so we need to find the height. We can use the Pythagorean theorem to find the height. Since the small triangle is a 30°-60°-90° triangle, the height (opposite the 30° angle) is half the length of the hypotenuse (opposite the 90° angle). Therefore, the height is 30√3 feet.

Using the formula for the area of a triangle:

Area = 1/2 * base * height
= 1/2 * 15 * 30√3
≈ 225√3 square feet

Rounding to the nearest tenth, the area of the small triangle is approximately 389.7 square feet.