Question

5. Бісектриса тупого кута паралелограма поділяє сторону на вiдрiзки 3см i 5 см, починаючи від вершини гострого кута. Знайти периметр паралелограма.​

Answer 1

Ответ:

22 см

Объяснение:

BK=3, KC=5, AK-биссектриса, ABCD-параллелограмм

ABCD-параллелограмм⇒AD||BC, AB=CD, BC=AD

AD||BC⇒∠KAD=∠AKB

AK-биссектриса⇒∠KAB=∠AKB

∠KAD=∠AKB=∠KAB⇒∠AKB=∠KAB⇒ΔABK-равнобедренный⇒AB=BK=3

BC=BK+KC=3+5=8

P(ABCD)=2(AB+BC)=2(8+3)=22

Answer 2

Bisector of an obtuse angle in a parallelogram

In order to find the perimeter of the parallelogram, we need to determine the lengths of the sides. Let's start by understanding the given information.

The bisector of an obtuse angle in a parallelogram divides the opposite side into two segments of lengths 3 cm and 5 cm, starting from the vertex of the acute angle.

To find the perimeter of the parallelogram, we need to determine the lengths of all four sides.

Let's denote the lengths of the sides as follows: - Side 1: a - Side 2: b - Side 3: c - Side 4: d

Since a parallelogram has opposite sides that are equal in length, we can conclude that: - Side 1 is equal to Side 3 (a = c) - Side 2 is equal to Side 4 (b = d)

Now, let's use the information about the bisector of the obtuse angle to find the lengths of the sides.

The bisector divides the opposite side into two segments of lengths 3 cm and 5 cm. Let's denote the length of the entire opposite side as x.

According to the given information, we have the following equation: 3 cm + 5 cm = x

Simplifying the equation, we get: 8 cm = x

Now, we can determine the lengths of the other sides using the fact that opposite sides of a parallelogram are equal.

Since Side 1 is equal to Side 3, and Side 3 is equal to x, we have: a = c = x = 8 cm

Similarly, since Side 2 is equal to Side 4, and Side 2 is equal to the sum of the two segments of the opposite side (3 cm + 5 cm), we have: b = d = 3 cm + 5 cm = 8 cm

Therefore, all four sides of the parallelogram have a length of 8 cm.

To find the perimeter of the parallelogram, we add the lengths of all four sides: Perimeter = Side 1 + Side 2 + Side 3 + Side 4 Perimeter = a + b + c + d Perimeter = 8 cm + 8 cm + 8 cm + 8 cm Perimeter = 32 cm

Therefore, the perimeter of the parallelogram is 32 cm.