Final answer:
The diagonal of a parallelogram can be found using the law of cosines, but the solution 7a does not match the provided options. A probable mistake exists in the question's specifications or given options.
Step-by-step explanation:
The subject of this question is the calculation of the diagonal of a parallelogram with adjacent sides of 4a and 3a, and the angle between them is 60°. To solve this, we will use the formula for calculating the diagonal of a parallelogram, which is derived from the law of cosines (which is a generalization of the Pythagorean theorem).
D = sqrt[a² + b² + 2ab cos(θ)] (where D is the diagonal, a and b are the sides, and θ is the included angle).
Substituting the given values, we get D = sqrt[(4a)² + (3a)² + 2*(4a)*(3a)*cos(60°)].
This simplifies to D = sqrt[16a² + 9a² + 24a²] = sqrt[49a²] = 7a.
Unfortunately, this answer does not match any of the given options, suggesting a possible mistake in the question's specifications or the options provided.
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