Найдите площадь треугольника ABCD, если BC=8 CE=3 и его периметр равен 56.
First, draw a diagram of the triangle ABCD with BC=8 and CE=3. Then, use the Pythagorean theorem to find the length of AC, which is the hypotenuse. AC=√(AB^2+BC^2)=√(8^2+3^2)=√73. Also, since the perimeter is 56, we can set up an equation: AB+BC+CD=56. Substituting our given values, we get AB+8+√73=56, which gives us AB=48-√73. Now, using the formula for the area of a triangle, we get A=1/2*base*height. Since the base is AB=48-√73, we need to find the height. Drawing a perpendicular line from B to AC, we create a right triangle with the hypotenuse being AC=√73. Using the Pythagorean theorem again, we get the height as √(√73^2-8^2)=√57. Therefore, the area of triangle ABCD is A=(48-√73)*√57/2≈42.125.
