Question

У прямокутний трикутник вписаний квадрат, який має з ним спільний кут. Знайди площу квадрата, якщо катети трикутника дорівнюють 15 м та 10 м. Вирішіть, будь ласка, з дано та малюнком

Answer 1

To find the area of the square inscribed in a right triangle, we can use the relationship between the side lengths of the triangle and the square. Let's solve this problem step by step.

Step 1: Understand the problem

We are given a right triangle with legs measuring 15 m and 10 m. The triangle is inscribed in a square, and the square shares one angle with the triangle. We need to find the area of the square.

Step 2: Find the hypotenuse of the triangle

To find the hypotenuse of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using the given leg lengths of 15 m and 10 m, we can calculate the hypotenuse as follows:

c^2 = a^2 + b^2 c^2 = 15^2 + 10^2 c^2 = 225 + 100 c^2 = 325 c ≈ 18.03 m

So, the hypotenuse of the triangle is approximately 18.03 m.

Step 3: Find the side length of the square

Since the square is inscribed in the right triangle, the side length of the square is equal to the length of the hypotenuse.

Therefore, the side length of the square is approximately 18.03 m.

Step 4: Find the area of the square

To find the area of the square, we can use the formula:

Area = side length^2

Substituting the side length of the square, we get:

Area = 18.03^2 Area ≈ 325.81 m^2

Therefore, the area of the square is approximately 325.81 square meters.

I hope this helps! Let me know if you have any further questions.