Question

В трапеции абсд основания БС и АД равны 7 см и 14 см. АС равно 8 см. О - точка пересечения диагоналей. Найти АО

Answer 1

Рассмотрим треугольники АВС и АОД
ВС<АД в 2 раза следовательно треугольник ВСО в 2 раза меньше чем АОД. значит АО=6, т.к. ОС <АО в 2 раза.

Answer 2

Task: Find AO in a Trapezoid

To find AO in the given trapezoid, we need to use the information provided. Let's break down the given information:

- The lengths of the bases of the trapezoid, BS and AD, are 7 cm and 14 cm, respectively. - The length of side AC is 8 cm. - O is the point of intersection of the diagonals.

To find AO, we need to determine the length of the diagonal OD and subtract it from the length of the base AD.

Solution:

To find the length of the diagonal OD, we can use the properties of similar triangles. By drawing a line parallel to the bases of the trapezoid, we can create two similar triangles: AOD and BSC.

Let's denote the length of OD as x. Using the properties of similar triangles, we can set up the following proportion:

AD/BS = AO/SC

Substituting the given values:

14/7 = (14 - x)/8

Simplifying the equation:

2 = (14 - x)/8

Multiplying both sides by 8:

16 = 14 - x

Subtracting 14 from both sides:

2 = -x

Dividing both sides by -1:

x = -2

Since the length cannot be negative, we can disregard the negative sign. Therefore, the length of OD is 2 cm.

To find AO, we subtract the length of OD from the length of AD:

AO = AD - OD = 14 cm - 2 cm = 12 cm

Therefore, the length of AO is 12 cm.

Summary:

In the given trapezoid with bases BS and AD equal to 7 cm and 14 cm, respectively, and side AC equal to 8 cm, the length of AO is 12 cm.