Question

Медиана проведенная к гипотенузе прямоугольного треугольника 13 см .найдите стороны треугольника если его периметр равен 60 Ставлю 50 баллов сделайте быстреее заранее спасибо

Answer 1

Медиана прямоугольного тр-ка равна половине гипотенузы
С=90; AC - вертикальный катет; BC - горизонтальный
CO=13 - медиана; AB=26
Тр-ки COB и COA - равнобедренные
Из точки O опустим перпендикуляры ON и OM на катеты AC и BC соответственно. ON и OM являются и медианами
AC+BC=60-26=34
Пусть AC=x⇒BC=34-x
CO^2=CM^2+MO^2
CM=1/2*BC=(34-x)/2
MO=CN=1/2*AC=x/2⇒
(34-x)^2/4+x^2/4=169⇒1156-68x+x^2+x^2=676⇒
2x^2-68x+480=0⇒x^2-34x+240=0⇒
По теореме Виетта
x1+x2=34; x1*x2=240⇒
x1=24; x2=10
34-24=10
34-10=24
Один катет - 10, другой - 24

Answer 2

Finding the Sides of a Right Triangle with a Median to the Hypotenuse

To find the sides of a right triangle when the median to the hypotenuse is 13 cm and the perimeter is 60 cm, we can use the following steps:

1. Let's assume that the two legs of the right triangle are represented by the variables a and b. 2. The median to the hypotenuse divides the right triangle into two smaller triangles, each with a hypotenuse equal to half of the original hypotenuse. Therefore, the hypotenuse of each smaller triangle is 13 cm / 2 = 6.5 cm. 3. Using the Pythagorean theorem, we can express the relationship between the sides of the smaller triangles: - For the first smaller triangle: a^2 + b^2 = (6.5)^2 - For the second smaller triangle: a^2 + b^2 = (6.5)^2 4. The perimeter of the right triangle is the sum of the lengths of all three sides. In this case, the perimeter is 60 cm. Therefore, we can express the perimeter as: a + b + hypotenuse = 60. 5. Substituting the value of the hypotenuse (6.5 cm) into the perimeter equation, we get: a + b + 6.5 = 60. 6. Rearranging the equation, we have: a + b = 60 - 6.5.

Now, we have two equations: - a^2 + b^2 = (6.5)^2 - a + b = 60 - 6.5

We can solve these equations simultaneously to find the values of a and b.

Let's proceed with the calculations.