Question

Диагонали прямоугольникаАВСД пересекаются в точке О АВ=10см ВД=12см найдите периметр треугольника СОД

Answer 1

OD=BD:2=12:2=6см OC=OD=6см CD=AB=10см P=6+6+10=22см

Answer 2

Calculation of the Perimeter of Triangle SOD

To find the perimeter of triangle SOD, we need to know the lengths of its sides. Let's start by finding the length of side SO.

Given: - AB = 10 cm - BD = 12 cm

Since the diagonals of rectangle ABCD intersect at point O, we can conclude that AO = BO = CO = DO. Therefore, we can consider triangle AOB as an isosceles triangle.

Using the properties of an isosceles triangle, we can find the length of side AO (or BO) by dividing the length of BD by 2.

AO = BO = BD / 2 = 12 cm / 2 = 6 cm.

Next, let's find the length of side OD.

Since the diagonals of rectangle ABCD intersect at point O, we can conclude that CO = DO. Therefore, we can consider triangle COD as an isosceles triangle.

Using the properties of an isosceles triangle, we can find the length of side OD (or OC) by dividing the length of AB by 2.

OD = OC = AB / 2 = 10 cm / 2 = 5 cm.

Now, we have the lengths of all three sides of triangle SOD: - SO = AO = BO = 6 cm - OD = OC = 5 cm - SD = OD = 5 cm

To calculate the perimeter of triangle SOD, we add the lengths of all three sides:

Perimeter of triangle SOD = SO + OD + SD = 6 cm + 5 cm + 5 cm = 16 cm.

Therefore, the perimeter of triangle SOD is 16 cm.

Please let me know if there is anything else I can help you with!