Question

в прямоугольнике ABCD смежные стороны относятся как 3:4,а его диагональ равна 20 см. чему равна площадь этого треугольника срочно нужен ответ, пожалуйста!!????

Answer 1

Ответ: 192

Объяснение: (^ -знак степени)

Пусть  AB:BC=3:4,  AB=3x,  BC=4x,  из тр-ка АВС  AC^2=AB^2 +BC^2, (теор. Пифагора)

20^2 =(3x)^2+(4x)^2,   25x^2=400,  x^2=400/25,  x=20/5=4,  тогда,

AB=3*4=12,  BC=4*4=16,  S=AB*BC=12*16=192

Answer 2

Calculation of the Triangle's Area

To find the area of the triangle in the rectangle ABCD, we need to determine the lengths of the sides of the triangle. Given that the adjacent sides of the rectangle are in a ratio of 3:4 and the diagonal is 20 cm, we can use this information to calculate the lengths of the sides.

Let's assume that the shorter side of the rectangle is 3x and the longer side is 4x. Using the Pythagorean theorem, we can find the value of x:

Step 1: Apply the Pythagorean theorem to the sides of the rectangle ABCD: - The shorter side squared plus the longer side squared equals the diagonal squared. - (3x)^2 + (4x)^2 = 20^2

Simplifying the equation: - 9x^2 + 16x^2 = 400 - 25x^2 = 400 - x^2 = 400/25 - x^2 = 16 - x = √16 - x = 4

Now that we have the value of x, we can calculate the lengths of the sides of the triangle:

Step 2: Calculate the lengths of the sides of the triangle: - The shorter side of the triangle is 3x = 3 * 4 = 12 cm. - The longer side of the triangle is 4x = 4 * 4 = 16 cm.

Step 3: Calculate the area of the triangle using Heron's formula: - Heron's formula states that the area of a triangle with sides a, b, and c is given by: - Area = √(s * (s - a) * (s - b) * (s - c)) - where s is the semi-perimeter of the triangle, given by s = (a + b + c) / 2.

In this case, the sides of the triangle are 12 cm, 16 cm, and the diagonal of the rectangle (which is also the hypotenuse of the triangle) is 20 cm.

- The semi-perimeter s = (12 + 16 + 20) / 2 = 48 / 2 = 24 cm.

Now we can calculate the area of the triangle: - Area = √(24 * (24 - 12) * (24 - 16) * (24 - 20)) - Area = √(24 * 12 * 8 * 4) - Area = √(9216) - Area = 96 cm².

Therefore, the area of the triangle in the rectangle ABCD is 96 cm².

Please note that the calculation assumes the triangle is a right triangle, as it is formed by the diagonal of the rectangle.