The figure below is a square. What is its perimeter (measured in units

Question

The figure below is a square. What is its perimeter (measured in units)? 2014-12-04_1851.png A) 6 \sqrt{2} B) 9 C) 12 D) 12 \sqrt{2} E) 18 Source: Chili Hot GMAT

hopeful101candidate · Answer

The figure below is a square. What is its perimeter (measured in units)?

From the figure, we can see that the diagonal of the square measures 3 units, which corresponds to the 90 degree angle. Therefore, the measure of each side of the square is 3/sqrt(2) units. The perimeter would then be: 4 * 3/sqrt(2) = 12/sqrt(2). If you simplify, you get: 12*sqrt(2)/2, which equals 6*sqrt(2).

Answer is A.

smartyguy · Answer

The figure below is a square. What is its perimeter (measured in units)?

Attachment:

img.png [ 4.67 KiB | Viewed 5900 times ]

A) 6 \(\sqrt{2}\)
B) 9
C) 12
D) 12 \(\sqrt{2}\)
E) 18

Draw the diagonal first horizontal or vertical your wish.

AS we know sides of a square make 90 degree angle.

so the length of the diagonal is 3 as mentioned with the help of a diagonal we can find the side of the square.

their are two ways to find a side of the square :

1) using the triangle property of 45:45:90
from which we can easily find the side i.e \(\frac{3}{\sqrt{2}}\)

2) By using the diagonal formula i.e \(\sqrt{2}*a\) = diagonal ---> where a is the side of the square.

from here we can easily find the side i.e \(\frac{3}{\sqrt{2}}\)

So the perimeter of the square is\(4*\frac{3}{\sqrt{2}}\) = 6 \(\sqrt{2}\) Ans!

Hence A! ans

Regards
SG

AliciaSierra · Answer

Length of the any diagonal of square = side of square *  \sqrt{2} 
Length of diagonal of below square = 3
Let us say side of below square is  S 
 
so  S   \sqrt{2}   = 3

S =   \frac{3}{\sqrt{2}}

Perimeter =  S*4  =  \frac{3}{\sqrt{2}} *4 =  6*\sqrt{2}

Answer : A

peachfuzz · Answer

We know that the small triangle near the origin is a 45-45-90 triangle. We know the short sides of the triangle has length of 1.5. This makes the Hypotenuse (side of the square)  1.5 \sqrt{2}  . Multiply  1.5 \sqrt{2}  by 4 and we get A)  6 \sqrt{2}

PareshGmat · Answer

Answer = A) 6 \sqrt{2} Refer diagram below: 2014-12-04_1851.png Perimeter of square = 4 * \sqrt{1.5^2 + 1.5^2} = 4 * \sqrt{4.5} = \sqrt{72} = 6\sqrt{2}

Bunuel · Answer

The correct answer is A.

intheend14 · Answer

Since we have a square, we can identify that the diagonals are equal to 3. This means the sides equal 3/sqrt(2). So, the perimeter is simply 2 times the length of a side or 4*3/sqrt(2) = 4*3*sqrt(2)/2 = 6*sqrt(2).

Choice A

Choice A

mathiaskeul · Answer

a^2+b^2=c^2

In the left bottom corner there is a right triangle, from which we know that it measures on the a- and b-sides.

1.5^2+1.5^2=(3/2)^2+(3/2)^2= 9/4+9/4 = 4.5 OF 9/2

sqrt(9/2)= 3/sqrt(2)

simplifying by multiplying top and bottom by sqrt(2)

3sqrt(2)/2

4 times 3sqrt(2)/2 is 12sqrt(2)/2 is 6sqrt(2)

Answer is A

Abhishek009 · Answer

In the figure length of the diagonal is 3 units.

We know that for a square diagonals are always equal and length of a diagonal is  a√2  { a = sides of a square }

So, lets workout -

a√2 = 3
a = 3/√2

=> 4a=12/√2

=> √2*12/2

=> 6√2

Hence answer is (A)

powellmittra · Answer

Area = D^2/2 = 9/2
Length = sqrt (9/2)

Perimeter = 3/sqrt(2)*4 = 6 sqrt(2)

is this solution correct?

Donnie84 · Answer

Another approach:

Let's look at the 2 vertices of the square that lie on x and y axes. Distance between the 2 points will give us the length of the side of the square and we can calculate the perimeter.

The 2 vertices are at the midpoints and their coordinates will be (1.5,0) and (0,1.5) since coordinates of a midpoint are the average of the coordinates of the end points.

Distance between the vertices = sq root (2*9/4) or 3/2 sq root (2).
Multiple this by 4 we get 6 sq root (2).

Answer (A).

chetan2u · Answer

Yes, your approach is correct.. :good

bumpbot · Answer

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The figure below is a square. What is its perimeter (measured in units

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The figure below is a square. What is its perimeter (measured in units

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