Question: The diagonal length of a square is 14.1 sq. units. What is the area of the square, rounded to the nearest integer? (√2 is approximately 1.41)

A. 96
B. 97
C. 98
D. 99
E. 100

Answer: D

Solution and Explanation:

Approach Solution 1:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with geometry. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
The square is divided into two congruent (equal) right triangles by a diagonal if an is the length of one of the square's sides. When any triangle is subjected to the Pythagorean Theorem, the result is diagonal² = side² + side² = a² + a² = 2a². Diagonal = a 2 results from taking the square root of both sides of this equation. The fact is that 14.1 is the diagonal length. Hence, a = 14.1/sqrt(2) = 14.1 (2)
The area, a², is now equal to [14.1/sqrt(2)]² ==> 14.1² / 2
==> 198.81/2 => 99.4
The closest number to 99 is 99.4. So,
Correct option: D

Approach Solution 2:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with geometry. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
There is a shortcut to this question.
We can remember that the area of a square (also known as the area of a rhombus) equals half of the product of diagonals rather than having to calculate the sides of a square. →
Area = d²/2 = 14.1² / 2 = 99.4 --> area is equal to 99 when rounded to the nearest integer.
Correct option: D

Approach Solution 3:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with geometry. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Let's first find the length of one side of the square using the diagonal length.
The diagonal of a square is the hypotenuse of a right triangle with legs that are the sides of the square. Therefore, we can use the Pythagorean theorem to find the length of one side:
s² + s² = (14.1)²
2s² = (14.1)²
s² = (14.1)² / 2
s = √((14.1)² / 2) (taking the positive root since s is a length)
s ≈ 9.979
Now that we know the length of one side of the square, we can use it to find the area:
Area = s² ≈ (9.979)² ≈ 99.4
Rounding to the nearest integer, we get 99.
Correct option: D

“The diagonal length of a square is 14.1 sq. units. What is the area of" - 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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