Rational Area and Irrational Perimeter Question for a Rhombus

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Option d: a rhombus with a side length units and diagonals with lengths units and units

Explanation:

The formula to find the area of the rhombus is where p,q are diagonals.

The formula to find the perimeter of the rhombus is where a is the side length.

Now, we shall determine the rhombus which have a rational area and an irrational perimeter.

Option a: a rhombus with a side length 5 units and diagonals with lengths 8 units and 6 units

Area =

Perimeter =

This is a rhombus with a rational area and a rational perimeter.

Hence, Option a is not the correct answer.

Option b: a rhombus with a side length units and diagonals with lengths units and units

Area =

Perimeter =

This is a rhombus with irrational area and irrational perimeter.

Hence, Option b is not the correct answer.

Option c: a rhombus with a side length units and diagonals with lengths units and units

Area =

Perimeter =

This is a rhombus with rational area and irrational perimeter.

Hence, Option c is the correct answer.

Option d: a rhombus with a side length 2.5 units and diagonals with lengths units and units

Area =

Perimeter =

This is a rhombus with an irrational area and a rational perimeter.

Hence, Option d is not the correct answer.

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