Question: The perimeter of a rhombus is 44. What is the maximum area the rhombus could have?

1. 121
2. 144
3. 169
4. 196
5. 225

Answer: A

Solution and Explanation:

Approach Solution 1:

Given that the perimeter of a rhombus is 44. It has asked to find out the maximum value of area the rhombus can have.

the largest possible surface area that a geometric object can have when it has a symmetrical shape.

Therefore, in order to have the maximum possible area for rhombus, it needs to be square and each side needs to be 11. (Perimeter -44)

Therefore, the maximum size of rhombus will equal the area of the square, which is equal to 11 times 11 or 121.

A is the correct choice.

Approach Solution 2:

Given:
A rhombus has a perimeter that is equal to 44.

To Find:
The largest possible surface area that the rhombus could have.
Strategy and Planning of Action

The greatest area that a rhombus can have when it's a square and the perimeter is supplied.
The perimeter of a square = 44
Side = 44 / 4 = 11
Area = 11^2 = 121

A is the correct choice.

Approach Solution 3:

44 is the value of the rhombus's perimeter. What is the largest possible surface area that the rhombus can have?

44/4 equals 11 on both sides.

If the diagonals are equal to each other, the area will be at its maximum of 1 if they bisect each other.

3. they cut through the middle at right angles
   Therefore, the value of a portion of the diagonal that was calculated is x=111/2 times x=111/2.

Diagonal 1= diagonal2 = 2x
The area of the rhombus can be calculated as: diagonal 1 times diagonal 2 times ½
Area= 2 * 11 * 11 * 1/2 * ½
Area = 121

A is the correct choice.

“The perimeter of a rhombus is 44. What is the maximum area the rhombus" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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