Question

29. Бісектриса кута прямокутника ділить його діагональ на відрізки завдовжки 4 см і 12 см. Знайдіть площу прямокутника (у см?). Відповідь.

Answer 1

Ответ:

76,8 см кв

Пошаговое объяснение:

По свойству биссектрисы стороны прямоугольника относятся как 12:4=3:1

Пусть одна сторона х другая 3х. Диагональ 12+4=16 см.

По теореме Пифагора  (9+1)*х*х=16*16

х*х=16*16/10

Площадь прямоугольника

3х*х=3*16*16/10=48*16/10=76,8 см кв

Answer 2

Ответ: 76.8см²

Пошаговое объяснение:

Значит, по свойству биссектрисы. если коэффициент пропорциональности х, то одна сторона 4х, другая 12х, а по теореме Пифагора

16х²+144х²=16²

160х²=256⇒х²=256/160=1.6

площадь прямоугольника равна 4х*12х=48х²=48*1.6=76.8/см²/

Answer 3

Bisector of a Rectangle's Angle

To find the area of a rectangle, we need to know the lengths of its sides. In this case, we are given that the bisector of one of the rectangle's angles divides its diagonal into segments of length 4 cm and 12 cm. Let's denote the lengths of the sides of the rectangle as a and b.

Finding the Lengths of the Sides

Since the bisector of the angle divides the diagonal into segments of length 4 cm and 12 cm, we can use this information to find the lengths of the sides of the rectangle.

Let's consider the diagonal of the rectangle as the hypotenuse of a right triangle, with the segments formed by the bisector as the legs. Using the Pythagorean theorem, we can find the lengths of the sides.

According to the Pythagorean theorem, the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

So, we have:

a^2 + b^2 = 4^2 + 12^2

Simplifying the equation, we get:

a^2 + b^2 = 16 + 144

a^2 + b^2 = 160

Finding the Area of the Rectangle

The area of a rectangle is given by the formula: Area = length × width.

In this case, the lengths of the sides of the rectangle are a and b. So, the area of the rectangle can be calculated as:

Area = a × b

To find the area, we need to know the values of a and b. From the previous equation, we have:

a^2 + b^2 = 160

Unfortunately, we don't have enough information to determine the exact values of a and b. We can only find the area in terms of a and b.

Therefore, the answer to the question "Find the area of the rectangle (in cm?)" cannot be determined without additional information.

If you have any further questions, feel free to ask!