Question

Сторона АБ прямоугольной трапеции АБСД с прямым углом А равна 7, диагональ БД=11.Найдите АД

Answer 1

Объяснение:

ABCD -трапеция; ∠А=90°

АВ=7 ; ВD=11

АD=?

∆ABD -прямоугольный:

по теореме Пифагора:

АD=√(BD²-AB²)=√(11²-7²)=√72=6√2

Answer 2

Finding the length of AD in a rectangular trapezoid ABCD

To find the length of AD in a rectangular trapezoid ABCD, we are given the following information: - Side AB is equal to 7. - Diagonal BD is equal to 11.

Let's use the given information to find the length of AD.

Solution:

In a rectangular trapezoid, the diagonals are perpendicular to each other and divide the trapezoid into four right triangles. Let's label the points as shown in the diagram below:

      A _______ B
       |       |
       |       |
       |_______|
      D         C

We are given that AB = 7 and BD = 11. We need to find the length of AD.

Using the Pythagorean theorem, we can find the length of AD. In right triangle ABD, we have:

AB^2 + AD^2 = BD^2

Substituting the given values, we get:

7^2 + AD^2 = 11^2

49 + AD^2 = 121

AD^2 = 121 - 49

AD^2 = 72

Taking the square root of both sides, we find:

AD = √72

Simplifying the square root, we get:

AD ≈ 8.49

Therefore, the length of AD in the rectangular trapezoid ABCD is approximately 8.49.

Answer:

The length of AD in the rectangular trapezoid ABCD is approximately 8.49.