If The Length of a Diagonal of a Square is 2√x, What is the Area GMAT Problem Solving

Question: If the length of a diagonal of a square is 2√x, what is the area of the square in terms of x ?

1. √x
2. √2x
3. 2√x
4. x
5. 2x

Correct Answer: E

Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:

• The length of a diagonal of a square is 2√x

Find out:

• The area of the square in terms of x

Let us assume a relationship between the diagonal and the side of a square.

According to that assumption,
The side of the square is 's'.

The relation between the side of a square and its diagonal (d) is 'd= s √2
Hence, s√2= 2 √x

These two will be equal because we are discussing the length of the same diagonal.

\(s=\frac{2\sqrt x}{\sqrt2}\)
Since the area of a square is \(s^2\), let us square both the sides

\(s^2=\frac{4x}{2}\)

\(s^2=2x\) (Area of Square)

Therefore, the area of the square in terms of x is 2x.

Approach Solution 2:
The problem statement informs that:
Given:

• The length of a diagonal of a square is 2√x

Find out:

• The area of the square in terms of x

Since it's given in the question it is a square we will get an isosceles right triangle with the diagonal and the sides will be in the ratio

1:1:√2
?:?:2√x

The square side will be 2√x/√2
Square this for Area 4x/2
=2x

Therefore, the area of the square in terms of x is 2x.

Approach Solution 3:
The problem statement informs that:
Given:

• The length of a diagonal of a square is 2√x

Find out:

• The area of the square in terms of x

The area of a square with a diagonal length of d is as follows:
A = d^2/2 (as per the rule of mathematics)

Therefore, the area of the square in question is (2√x)^2 / 2 = (4x)/2 = 2x.

Therefore, the area of the square in terms of x is 2x.

“If the length of a diagonal of a square is 2√x, what is the area”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “Foundations of GMAT Math”. GMAT Problem Solving questions enable the candidates to evaluate data and interpret numerical problems. GMAT Quant practice papers help the candidates to get familiar with several sorts of questions that will enable them to improve their mathematical learning.

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