Question

Прямоугольный треугольник имеет одинаковый периметр, как и прямоугольник высота которого 15 см. Посчитайте размер диагонали и площадь прямоугольника если вам известно, что сатет большой и гипотенуза прямоугольного треугольника равны 24 см и 25 см. Спасибо за помощь!!!!

Answer 1

другой катет по т.Пифагора sqrt(25^2-24^2)=7

P=24+7+25=56

 

P=2(a+b)

b=P/2-a=28-15=13

S=ab=195

d=sqrt(a^2+b^2)=sqrt(13^2+15^2)=sqrt(394)

Answer 2

Calculation of the Diagonal and Area of the Rectangle

To calculate the diagonal and area of the rectangle, we need to use the given information about the right-angled triangle and the height of the rectangle.

Let's start by finding the length and width of the rectangle using the given height of 15 cm. Since the perimeter of the rectangle is the same as that of the right-angled triangle, we can use this information to find the dimensions of the rectangle.

Let's assume the length of the rectangle is L and the width is W.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(L + W)

Since the perimeter of the rectangle is the same as that of the right-angled triangle, we can write:

2(L + W) = 24 + 25

Simplifying the equation:

2L + 2W = 49

Now, let's find the dimensions of the rectangle.

We know that the height of the rectangle is given as 15 cm. Since the height of the rectangle is the same as the length of the right-angled triangle, we can write:

L = 15

Substituting this value into the equation we derived earlier:

2(15) + 2W = 49

Simplifying the equation:

30 + 2W = 49

2W = 49 - 30

2W = 19

W = 19/2

W = 9.5

So, the width of the rectangle is 9.5 cm.

Now, let's calculate the diagonal of the rectangle.

The diagonal of a rectangle can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the rectangle is the hypotenuse of the right-angled triangle, and the sides of the triangle are given as 24 cm and 25 cm.

Let's assume the diagonal of the rectangle is D.

Using the Pythagorean theorem, we can write:

D^2 = 24^2 + 25^2

Simplifying the equation:

D^2 = 576 + 625

D^2 = 1201

Taking the square root of both sides:

D = √1201

D ≈ 34.64

So, the diagonal of the rectangle is approximately 34.64 cm.

Finally, let's calculate the area of the rectangle.

The area of a rectangle is given by the formula:

Area = Length × Width

Substituting the values we found earlier:

Area = 15 × 9.5

Area = 142.5

So, the area of the rectangle is 142.5 square cm.

To summarize: - The diagonal of the rectangle is approximately 34.64 cm. - The area of the rectangle is 142.5 square cm.

Please note that the calculations are based on the given information and assumptions made.