Question

Дан параллелограмм ABCD. AD=6, AC=9, BD=5, AB=?

Answer 1

О+точка пересечения диагоналей (см.рисунок)
Рассмотрим Δ АДО
АД=6
АО=АС/2=9/2=4,5
ДО=ДВ/2=5/2=2,5

По трем сторонам найдем косинус угла АДО
АО²=ДО²+АД²-2ДО*АД* cos АДО
2ДО*АД* cos АДО=-АО²+ДО²+АД²
cos АДО=(-АО²+ДО²+АД²)/(2ДО*АД)=(-4,5²+2,5²+6²)/(2*2,5*6)=22/30=11/15

Рассмотрим Δ АДВ
АД=6
ДВ=5
cos АДВ=11/15

Найдем АВ
АВ=√(АД²+ДВ²-2*АД*ДВ*cos АДВ)=√(6²+5²-2*5*6*11/15)=√17≈4,12... где-то я ошиблась...мне кажется...

Answer 2

Given the parallelogram ABCD, where AD = 6, AC = 9, BD = 5, we need to find the length of AB.

To find the length of AB, we can use the properties of a parallelogram. In a parallelogram, opposite sides are equal in length. Therefore, we can conclude that AB is equal to CD.

Let's analyze the given information:

AD = 6 AC = 9 BD = 5

Since AD is opposite to BC and AC is opposite to BD, we can conclude that BC = AD = 6 and BD = AC = 9.

Now, let's use the fact that opposite sides of a parallelogram are equal to find the length of AB. We know that AB is equal to CD, and we have already found that BC = AD = 6. Therefore, AB = 6.

Hence, the length of AB is 6.