Question

Периметр трикутника MNK дорівнює 64 см; NK = 24 см, а сторона МК в 1,5 раза менша, ніж MN. Доведіть, що кут М = куту К.

Answer 1

Ответ:

кут М= кутуК так яка трикутник рівнобедрений.

Объяснение:

детально на фото

Answer 2

Given Information

We are given the following information about triangle MNK: - Perimeter of triangle MNK is 64 cm. - Length of side NK is 24 cm. - Side MK is 1.5 times smaller than side MN.

Solution

To prove that angle M is equal to angle K, we need to use the given information and apply some geometric principles.

Let's start by assigning variables to the lengths of the sides: - Let MN = x cm (length of side MN) - Let MK = 1.5x cm (length of side MK) - Let NK = 24 cm (length of side NK)

We know that the perimeter of a triangle is the sum of the lengths of its sides. So we can write the equation for the perimeter of triangle MNK as:

x + 1.5x + 24 = 64

Simplifying the equation, we get:

2.5x + 24 = 64

Subtracting 24 from both sides, we have:

2.5x = 40

Dividing both sides by 2.5, we get:

x = 16

Now that we know the length of side MN is 16 cm, we can find the length of side MK:

MK = 1.5x = 1.5 * 16 = 24 cm

We can see that the length of side MK is equal to the length of side NK. Since the lengths of two sides of a triangle are equal, the angles opposite those sides are also equal. Therefore, angle M is equal to angle K.

Thus, we have proved that angle M is equal to angle K.

Note: The sources provided did not contain specific information related to this problem. The solution is derived using basic geometric principles and algebraic equations.