Question

Найдите площадь прямоугольного треугольника, если его катет и гипотенуза равны соответственно 28 и 100.

Answer 1

1) По условию нам дан прямоугольный △АВС, то по теореме Пифагора АС^2=АВ^2 - BC^2; АС^2= 100^2 - 28^2=10000 - 784=9216 => АС=96
2)S△АВС= 1/2*АС*СВ; S△АВС= 1/2*96*28= 1/2*2688= 1344
Ответ: 1344

Answer 2

Finding the Area of a Right Triangle

To find the area of a right triangle, we can use the formula: Area = (1/2) * base * height.

In this case, the given triangle has a leg (or base) of 28 and a hypotenuse of 100.

Using the formula, we can calculate the area as follows:

Area = (1/2) * 28 * height

To find the height, 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.

In this case, the hypotenuse is 100, and one of the legs is 28. Let's call the height of the triangle 'h'.

According to the Pythagorean theorem, we have:

28^2 + h^2 = 100^2

Simplifying the equation, we get:

h^2 = 100^2 - 28^2

Now, let's calculate the value of 'h':

h^2 = 10000 - 784

h^2 = 9216

Taking the square root of both sides, we find:

h = sqrt(9216)

h = 96

Now that we have the height, we can calculate the area of the triangle:

Area = (1/2) * 28 * 96

Area = 1344 square units

Therefore, the area of the given right triangle with a leg of 28 and a hypotenuse of 100 is 1344 square units.