Question

На стороне AD параллелограмма ABCD взята точка е Так что ае равно 4 см и D 5 см и 12 см в д 13 см Докажите что треугольник BCD прямоугольный Найдите площадь параллелограмма. Помогите пожалуйста очень очень надо!!)

Answer 1

П/у - прямоугольный, парал-м - параллелограмм
Если по теореме Пифагора сходится все, то значит, что треугольник прямоугольный

Answer 2

Given Information:

We are given a parallelogram ABCD, where point E is taken on the side AD such that AE = 4 cm and AD = 5 cm. Additionally, we are given that CD = 12 cm and BD = 13 cm.

Proof that Triangle BCD is Right-angled:

To prove that triangle BCD is right-angled, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we can consider triangle BCD as a right-angled triangle, with CD as the hypotenuse. We need to show that the square of CD is equal to the sum of the squares of BC and BD.

Let's calculate the lengths of BC and BD using the given information:

Since ABCD is a parallelogram, opposite sides are equal. Therefore, BC = AD = 5 cm.

Using the given information, we know that BD = 13 cm.

Now, let's calculate the square of CD and the sum of the squares of BC and BD:

CD^2 = 12^2 = 144 BC^2 + BD^2 = 5^2 + 13^2 = 25 + 169 = 194

Since CD^2 = BC^2 + BD^2, we can conclude that triangle BCD is right-angled.

Finding the Area of the Parallelogram:

To find the area of the parallelogram ABCD, we can use the formula: Area = base * height.

In this case, the base of the parallelogram is BC, which we have already calculated as 5 cm.

To find the height, we can use the formula for the area of a triangle: Area = (1/2) * base * height.

Since triangle BCD is right-angled, we can use the lengths of BC and BD as the base and height, respectively.

Therefore, the area of the parallelogram ABCD is given by:

Area = BC * BD = 5 cm * 13 cm = 65 cm^2.

So, the area of the parallelogram is 65 square centimeters.

I hope this helps! Let me know if you have any further questions.