Question

СРОЧНО !!! С ДЕЙСТВИЯМИ биссектриса угла А прямоугольника ABCD пересекает его диагональ BD в точке Р, причем ВР: РD = 2: 3. Найдите площадь этого прямоугольника в км ^ 2, если его периметр равен 40 км.

Answer 1

Получится 20
биссектриса это крыса бегуящая по углам и делит их по полам

Answer 2

Finding the Lengths of the Sides of the Rectangle

To find the area of the rectangle, we first need to determine the lengths of its sides. Let's denote the length of side AB as a and the length of side BC as b.

Since the bisector of angle A intersects diagonal BD at point P, and the ratio of VP to PD is given as 2:3, we can use this information to find the lengths of the sides.

Let's assume that VP is 2x and PD is 3x, where x is a common factor. Therefore, we have VP = 2x and PD = 3x.

According to the properties of a rectangle, the diagonals are equal in length. Therefore, we can equate the lengths of diagonals BD and AC.

BD = AB + AD

Since AD is equal to BC, we can rewrite the equation as:

BD = AB + BC

Substituting the values of VP and PD, we get:

2x + 3x = AB + BC

Simplifying the equation, we have:

5x = AB + BC

Since the perimeter of the rectangle is given as 40 km, we can write another equation:

2(AB + BC) = 40

Simplifying this equation, we have:

AB + BC = 20

Now we have a system of equations:

5x = AB + BC AB + BC = 20

We can solve this system of equations to find the values of AB and BC.

Solving the System of Equations

To solve the system of equations, we can use substitution or elimination. Let's use the substitution method.

From the second equation, we can express BC in terms of AB:

BC = 20 - AB

Substituting this value into the first equation, we have:

5x = AB + (20 - AB)

Simplifying the equation, we get:

5x = 20

Dividing both sides by 5, we find:

x = 4

Now we can substitute the value of x back into the equation BC = 20 - AB:

BC = 20 - AB BC = 20 - 4 BC = 16

Therefore, the length of side BC is 16 km.

Substituting the value of x into the equation AB + BC = 20, we find:

AB + BC = 20 AB + 16 = 20 AB = 4

Therefore, the length of side AB is 4 km.

Calculating the Area of the Rectangle

Now that we know the lengths of the sides AB and BC, we can calculate the area of the rectangle.

The area of a rectangle is given by the formula:

Area = Length * Width

In this case, the length is AB (4 km) and the width is BC (16 km).

Therefore, the area of the rectangle is:

Area = 4 km * 16 km = 64 km^2

So, the area of the rectangle is 64 km^2.

Please let me know if there's anything else I can help you with!