Answer:
Step-by-step explanation: Since ABCD is a rhombus, all sides are equal in length, and opposite angles are equal. Let's denote the length of each side as "s". We know that the area of a rhombus can be calculated as (diagonal1 * diagonal2)/2.
Using the given information, we can create the following diagram:
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A
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P-----------B
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C
We know that AC and BD are diagonals of the rhombus, and their lengths are in a 4:3 ratio. Let's denote the length of AC as 4x and the length of BD as 3x.
We also know that the length of side PA is equal to the length of side PB, and the length of side PC is equal to the length of side PD. Therefore, we can use the Pythagorean theorem to calculate the value of s:
s^2 = PA^2 + AP^2 = (4x)^2 + (s/2)^2
s^2 = PB^2 + BP^2 = (3x)^2 + (s/2)^2
s^2 = PC^2 + CP^2 = (4x)^2 + (s/2)^2
s^2 = PD^2 + DP^2 = (3x)^2 + (s/2)^2
We can simplify these equations to:
16x^2 + s^2/4 = s^2
9x^2 + s^2/4 = s^2
16x^2 + s^2/4 = s^2
9x^2 + s^2/4 = s^2
Combining like terms, we get:
s^2 = 64x^2/3
s^2 = 36x^2/5
Setting these two expressions equal to each other and solving for x, we get:
64x^2/3 = 36x^2/5
320x^2 = 108x^2
x^2 = 0
This result indicates that our assumption of a rhombus with given side length and diagonal ratio is not valid. Therefore, there is no unique solution for the area of ABCD.