Question

Площадь прямоугольного треугольника равна 180 квадратных см найдите катеты треугольника если известно что один из катетов больше второго на 31 см

Answer 1

Площадь прямоугольного тр-ка равна половине произведения катетов.
Значит в нашем тр-ке произведение катетов равно 180*2 = 360 кв.см
Пусть один катет равен хсм, тогда другой (х+31)см.
Составляем уравнение: х * (х + 31) = 360
х² +31х - 360 = 0
D = 31² + 360 *4=961+1440=2401=49²
× =(  -31 + 49)÷2 = 9
× = (-31 - 49)÷2 не явл. решением, т.к. отриц. число.
1) х + 31 = 9 = 31 = 40 см     Ответ: 40см, 9см

Answer 2

Finding the Catheti of a Right-Angled Triangle

To find the catheti of a right-angled triangle when the area is known to be 180 square cm and one cathetus is larger than the other by 31 cm, we can use the formula for the area of a right-angled triangle and the relationship between the catheti.

The formula for the area of a right-angled triangle is: Area = (1/2) * base * height.

Given that the area is 180 square cm, we can use this information to find the catheti of the triangle.

Calculation

Let's denote the smaller cathetus as x and the larger cathetus as x + 31.

Using the formula for the area of a right-angled triangle, we have: 180 = (1/2) * x * (x + 31)

Solving for x will give us the value of the smaller cathetus, and then we can find the larger cathetus by adding 31 to this value.

Solution

Solving the equation 180 = (1/2) * x * (x + 31) will give us the values of the catheti.

Citation

- Source " = 5^2 + 5^2, x = (5 + 5)= (25+25) = 50 = 25*2 = 52, : 5 , 52, 7,07 ."

Let's proceed with the calculation.