Question

CТОРОНА AD ПАРАЛЛЕЛОГРАММА ABCD РАВЕН 9 СМ,А ЕГО ДИАГОНАЛИ РАВНЫ 14 СМ И 10 СМ.ТОЧКА О ЯВЛЯЕТСЯ ТОЧКО ПЕРЕСЕЧЕНИЯ ДИАГОНАЛЕЙ.НАЙДИТЕ ПЕРИМЕТР ТРЕУГОЛЬНИКА BOC

Answer 1

Given Information:

We are given that the side AD of parallelogram ABCD is 9 cm, and its diagonals are 14 cm and 10 cm. Point O is the intersection point of the diagonals. We need to find the perimeter of triangle BOC.

Solution:

To find the perimeter of triangle BOC, we need to know the lengths of its sides. Let's use the given information to find the lengths of the sides.

Since ABCD is a parallelogram, opposite sides are equal in length. Therefore, side AB is also 9 cm.

We can use the Pythagorean theorem to find the length of side BC. In triangle BOC, BO and CO are the diagonals of the parallelogram ABCD. We are given that BO is 14 cm and CO is 10 cm. Let's find BC using the Pythagorean theorem:

BC^2 = BO^2 + CO^2

BC^2 = 14^2 + 10^2

BC^2 = 196 + 100

BC^2 = 296

BC = √296

BC ≈ 17.20 cm

Now we have the lengths of sides AB and BC. To find the perimeter of triangle BOC, we add the lengths of these sides:

Perimeter of triangle BOC = AB + BC + AC

Since AC is also equal to BC in a parallelogram, we can write:

Perimeter of triangle BOC = AB + 2 * BC

Perimeter of triangle BOC = 9 + 2 * 17.20

Perimeter of triangle BOC ≈ 43.40 cm

Therefore, the perimeter of triangle BOC is approximately 43.40 cm.