Question

ВС и АД основная трапеция АВСД .угол АВД равен углу ВСД. ВС= 4 см, ДС=6 см,ВД=8см.найти АД

Answer 1

Given Information

We are given a trapezoid ABCD, where angle AVD is equal to angle CVD. We are also given that VC = 4 cm, DS = 6 cm, and VD = 8 cm. We need to find the length of AD.

Solution

To find the length of AD, we can use the fact that the opposite sides of a trapezoid are parallel. Let's denote the length of AD as x.

Since VC is parallel to AD, we can use the property of similar triangles to set up a proportion. The triangles AVD and CVD are similar, so we can write:

VD / AD = VC / CD

Substituting the given values, we have:

8 cm / x = 4 cm / (x + 6 cm)

To solve for x, we can cross-multiply and solve the resulting equation:

8 cm * (x + 6 cm) = 4 cm * x

8x + 48 cm = 4x

4x = 48 cm

x = 12 cm

Therefore, the length of AD is 12 cm.