АВСД- прямокутник КА⟂(АВС) КВ=7см, КС=9см, КД=9см Знайти АК

To find AK, we need to use the Pythagorean theorem.

In rectangle ABCD, we have a right triangle AKD with sides AK, KD, and AD. Since KD = 9 cm, we need to find the length of AD.

Given that KV = 7 cm and KS = 9 cm, we can deduce that the triangle KVS is a right triangle.

Using the Pythagorean theorem in triangle KVS, we have:

KV^2 + KS^2 = VS^2 (7 cm)^2 + (9 cm)^2 = VS^2 49 cm^2 + 81 cm^2 = VS^2 130 cm^2 = VS^2

Therefore, VS = √130 cm.

Now, in triangle KAD, we have:

AK^2 + KD^2 = AD^2 AK^2 + (9 cm)^2 = AD^2 AK^2 + 81 cm^2 = AD^2

But we know that AD = KS + VS.

So, KS + VS = √130 cm + VS = AD.

Therefore,

AK^2 + 81 cm^2 = (√130 cm + VS)^2 AK^2 + 81 cm^2 = (√130 cm)^2 + 2 * √130 cm * VS + VS^2 AK^2 = 130 cm + 2 * √130 cm * √130 cm + VS^2 - 81 cm^2 AK^2 = 130 cm + 260 cm + VS^2 - 81 cm^2 AK^2 = 389 cm + VS^2 - 81 cm^2 AK^2 = 308 cm + VS^2

Substituting the value of VS^2 = 130 cm^2, we get:

AK^2 = 308 cm + 130 cm^2 AK^2 = 308 cm + 130 cm^2 AK^2 = 438 cm AK = √438 cm

Therefore, AK ≈ 20.93 cm.