diagonal of a square

[datonman]

The diagonal of square ABCD is 10. What is the average (arithmetic mean)of the area and the perimeter of the same square?

A.)37.14
B.)13.19
C.)39.14
D.)23.19

[Brent@GMATPrepNow]

The diagonal of square ABCD is 10. What is the average (arithmetic mean)of the area and the perimeter of the same square?

A.)37.14
B.)13.19
C.)39.14
D.)23.19

Let x = length of one side of square.

The diagonal of square ABCD is 10
So, x² + x² = 10²
Simplify: 2x² = 100
Divide both sides by 2 to get: x² = 50
Solve: x = √50

AREA of square = (side)(side)
= (√50)(√50)
= 50

PERIMETER of square = 4(side)
= 4√50

What is the average (arithmetic mean)of the area and the perimeter of the same square?
Average = (50 + 4√50)/2

NOTE: √49 = 7, so we can see that √50 = a little bit more than 7.
So, 4√50 = a little bit more than 28

So, Average = (50 + a little bit more than 28)/2
= (a little bit more than 78)/2
= a little bit more than 39
= C

Cheers,
Brent

[[email protected]]

Hi datonman,

What is the source of this question? While the individual 'pieces' of it (the basic Geometry rules involved) could be tested on your GMAT, the question and answer choices are oddly-designed. If you're actually studying for the GMAT, then you might want to invest in more realistic material.

GMAT assassins aren't born, they're made,
Rich

[ceilidh.erickson]

Rich is right - this is not a GMAT-like question, for the following reasons:

- GMAT PS questions will always give you 5 multiple choice answer choices, not 4.

- The GMAT will rarely ask you to do actual calculation that would yield an answer accurate to 2 decimal places. On a question like this, they would almost certainly ask for an approximate average, not an actual one. (The "correct" answer on this question is still approximate, btw, not actual, since the square root of 50 would yield a non-terminating decimal).