Question

Высота прямоугольного треугольника делит гипотенузу на отрезки длиной 18см и 32см. Найти площадь треугольника?

Answer 1

рассмотрим подобные треугольники
исходный (катеты a,b, гипотенуза c=18+32=50) , с катетом 18 см (катеты 18,h, гипотенуза а) и с катетом 32 см (катеты h,18 гипотенуза b)
a:b:50 = 18:h:a = h:32:b

b:50 = 32:b значит b = корень(50*32)=40

a:50 = 18:a значит а = корень(50*18)=30
площадь = a*b/2 = 40*30/2 = 600

 

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 height of the right triangle divides the hypotenuse into two segments, measuring 18 cm and 32 cm.

Let's calculate the area of the triangle using the given information.

Step 1: Identify the lengths of the base and height of the triangle. - The length of one segment of the hypotenuse is 18 cm. - The length of the other segment of the hypotenuse is 32 cm.

Step 2: Calculate the length of the hypotenuse. - The length of the hypotenuse can be found using 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 length of the hypotenuse as 'c', and the lengths of the other two sides as 'a' and 'b'. - According to the Pythagorean theorem, we have: c^2 = a^2 + b^2. - Substituting the given lengths, we get: c^2 = 18^2 + 32^2. - Solving for c, we find: c ≈ 36.055 cm.

Step 3: Calculate the area of the triangle. - Now that we have the lengths of the base (18 cm) and height (32 cm), we can use the formula for the area of a triangle: Area = (1/2) * base * height. - Substituting the values, we get: Area = (1/2) * 18 cm * 32 cm. - Calculating the area, we find: Area ≈ 288 cm^2.

Therefore, the approximate area of the given right triangle is 288 cm^2.