Question

Найдите площадь прямоугольного треугольника одна из сторон которого и гипотенуза равны соответственно 48 и 50

Answer 1

48^2+x^2=50^2x^2=50^2-48^2 = 2500-2304=196x= 14
Площадь прямоугольника будет = 48*14= 672 кв. см

Answer 2

Прямоугольник обзовем ABCD. AC - диагональ, AB - известная сторона. Надеюсь, сообразишь, как начертить. Диагональ и 2 стороны прямоугольника образуют прямоугольный треугольник, в котором известна гипотенуза и 1 катет. Для нахождения 2 катета (BC) воспользуемся теоремой Пифагора:
AD²=AB²+BC²
BC²=AD²-AB²
BC²=50²-48²
BC²=196
BC=√196
BC=14
Площадь прямоугольника равна произведению двух его сторон:
S=AB*BC=48*14=672

Answer 3

Finding the Area of a Right Triangle

To find the area of a right triangle, we can use the formula: Area = (base * height) / 2.

In this case, we are given that one of the sides and the hypotenuse of the right triangle are 48 and 50, respectively.

Let's use the given information to find the area of the triangle.

Solution:

We are given: - One side of the triangle (base) = 48 - The hypotenuse of the triangle = 50

To find the height 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.

Let's denote the height of the triangle as 'h'.

Using the Pythagorean theorem, we have:

48^2 + h^2 = 50^2

Simplifying the equation, we get:

2304 + h^2 = 2500

Subtracting 2304 from both sides, we have:

h^2 = 196

Taking the square root of both sides, we get:

h = 14

Now that we have the base (48) and the height (14), we can calculate the area of the triangle using the formula:

Area = (base * height) / 2

Substituting the values, we have:

Area = (48 * 14) / 2 = 672 / 2 = 336

Therefore, the area of the right triangle with one side measuring 48 and the hypotenuse measuring 50 is 336 square units.

Conclusion:

The area of the right triangle with one side measuring 48 and the hypotenuse measuring 50 is 336 square units.