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GMAT question - What is the approximate perimeter of a square that h... - Review

Type: Problem Solving

Difficulty: 4 star rating

What is the approximate perimeter of a square that has a diagonal of length 6?
  1. 4
  2. 13
  3. 17
  4. 20
  5. 24

Explanation

It is helpful if we draw a diagram for this.

Square with a diagonal of length 6

We can see that the diagonal, length 6, forms a right angled triangle with two of the sides of the square, length x, and so we can use the Pythagoras theorem to determine the length of those sides.

mathematical expression

Simplify both sides

mathematical expression

Divide both sides by 2

mathematical expression

Take the square root of both sides

mathematical expression

Now we know that mathematical expression and that mathematical expression so we can estimate that mathematical expression is just a bit greater than 4.

We know that the perimeter is equal to mathematical expression therefore we can estimate that the perimeter is somewhere around 16 or 17.

None of the answers is 16 and C is 17, so C is the correct answer.

Note: A quick check with a calculator reveals the answer to be 16.97... and so our estimate is very good.

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