Question

Найдите наименьшую высоту треугольника со сторонами, равным 17, 65, 80, и наибольшую высоту треугольника со сторонами , равным 13, 37целых 12 тринадцатых, 47 целых 1 тринадцатая прошу написать решение

Answer 1

Формула Герона S=N/представь это длинный корень кв/ под корнем p(p-a)(p-b)(p-c) - где р-полупериметр, a,b,c - стороны тр-ка С другой стороны площ. тр. находится, как произведение стороны на высоту и разделить пополам. Если возьмем a=80,b=65,c=17, то меньшая высота упадет на а, т.е. на большую сторону. Нарисуй и увидишь, почему. Пусть неизвестная высота h, тогда составим уравнение /площадь-то у него одна, приравняем площадь, вычесленную по одной формуле с площадью, вычесленной по другой формуле /S тогда не нужна/ 1/2ah= корню кв и под корнем полупериметр a+b+c/2 или 80+65+17 и разделить на 2 =81 Теперь из под корня 81 выйдет, как 9, а под корнем (81-80)(81-65)(81-17)=1х16х64=извлекаем корень=1х4х8=32 То есть в одной части уравнения площ. равна 9х32, пока оставим в таком виде. в другой части уравненияодна вторая 80хh что то же самое 40умнож на h Уравнение теперь выглядит 40h=9х32, сократим на 8 обе части/разделим на одно и то же число/, получим 5h=9х4 или 5h=36 h=7,2 см ответ меньшая высота = 7,2 см

Answer 2

Finding the Smallest Height of a Triangle

To find the smallest height of a triangle with sides of lengths 17, 65, and 80, we can use the formula for the area of a triangle. The area of a triangle can be calculated using the formula:

Area = (1/2) * base * height

In this case, the base of the triangle can be any of the three sides, and we are looking for the smallest height. To find the smallest height, we need to find the base that corresponds to the largest area.

Let's calculate the area of the triangle using each side as the base and find the corresponding height:

1. Using 17 as the base: - Area = (1/2) * 17 * height - Area = 8.5 * height

2. Using 65 as the base: - Area = (1/2) * 65 * height - Area = 32.5 * height

3. Using 80 as the base: - Area = (1/2) * 80 * height - Area = 40 * height

To find the smallest height, we need to find the base that corresponds to the largest area. Comparing the areas calculated above, we can see that the largest area is obtained when the base is 80. Therefore, the smallest height of the triangle is obtained when the base is 80.

Now, let's calculate the height using the base of 80:

- Area = 40 * height - Area = 40 * height = 40 * h

To find the height, we need to know the area of the triangle. Unfortunately, the area of the triangle is not provided in the question. Without the area, we cannot calculate the exact value of the height.

Answer 3

Finding the Smallest Height of a Triangle

To find the smallest height of a triangle with sides measuring 17, 65, and 80, we can use the formula for the area of a triangle. The area of a triangle can be calculated using the formula:

Area = (1/2) * base * height

In this case, the base of the triangle can be any of the three sides, and we are looking for the smallest height. To find the smallest height, we need to find the base that corresponds to the largest area.

Let's calculate the area of the triangle using each side as the base and find the corresponding height:

1. Using 17 as the base: - Area = (1/2) * 17 * height - Area = 8.5 * height

2. Using 65 as the base: - Area = (1/2) * 65 * height - Area = 32.5 * height

3. Using 80 as the base: - Area = (1/2) * 80 * height - Area = 40 * height

To find the smallest height, we need to find the base that corresponds to the largest area. Comparing the areas calculated above, we can see that the largest area is obtained when the base is 80. Therefore, the smallest height of the triangle is obtained when the base is 80.

Now, let's calculate the height using the base of 80:

- Area = 40 * height - Area = (1/2) * 80 * height - 40 * height = (1/2) * 80 * height - 40 = (1/2) * 80 - 40 = 40

Since the equation is true for any value of height, we can conclude that the smallest height of the triangle is 40.

Finding the Largest Height of a Triangle

To find the largest height of a triangle with sides measuring 13, 37 12/13, and 47 1/13, we can again use the formula for the area of a triangle. Using the same approach as before, we calculate the area of the triangle using each side as the base and find the corresponding height:

1. Using 13 as the base: - Area = (1/2) * 13 * height - Area = 6.5 * height

2. Using 37 12/13 as the base: - Area = (1/2) * (37 12/13) * height - Area = (1/2) * (37 + 12/13) * height - Area = (1/2) * (481/13) * height - Area = (240.5/13) * height

3. Using 47 1/13 as the base: - Area = (1/2) * (47 1/13) * height - Area = (1/2) * (47 + 1/13) * height - Area = (1/2) * (610/13) * height - Area = (305/13) * height

To find the largest height, we need to find the base that corresponds to the smallest area. Comparing the areas calculated above, we can see that the smallest area is obtained when the base is 13. Therefore, the largest height of the triangle is obtained when the base is 13.

Now, let's calculate the height using the base of 13:

- Area = 6.5 * height - Area = (1/2) * 13 * height - 6.5 * height = (1/2) * 13 * height - 6.5 = (1/2) * 13 - 6.5 = 6.5

Since the equation is true for any value of height, we can conclude that the largest height of the triangle is 6.5.

Therefore, the smallest height of the triangle with sides measuring 17, 65, and 80 is 40, and the largest height of the triangle with sides measuring 13, 37 12/13, and 47 1/13 is 6.5.