If a square has a diagonal of length b, what is the perimeter of the

Question

If a square has a diagonal of length  \sqrt{b} , what is the perimeter of the square?

A. 4b

B.  4\sqrt{2b}

C.  2\sqrt{\frac{b}{2}}

D.  \frac{4\sqrt{b}}{b}

E.  2\sqrt{2b}

GMATinsight · Answer

For a square with side a, diagonal = a√2

i.e. a√2 = √b
i.e. a = √(b/2)

Perimeter of square = 4a = 4*√(b/2) = 2*2*√(b/2) = 2*√(4b/2) = 2√(2b)

Answer: Option E

sudarshan22 · Answer

+1 for   E  .

Area of Square = Diagonal^2 / 2 = √b^2 / 2 = b/2
Area of Square = S^2 = b/2 --> S = √b / √2
Perimeter of Square = 4 * S = (4 * √b) / √2 = ((√2*√2*√2*√2) * √b) / √2 = √2*√2*√2 * √b = 2* √2 * √b = 2√2b

Hence,   E  .

generis · Answer

Perimeter of a square =  4s

Side of the square is derived from the diagonal*. This square: diagonal,  d=\sqrt{b} 
The diagonal of any square 
 d=s\sqrt{2}  so
 \sqrt{b}=s\sqrt{2} 
 \frac{\sqrt{b}}{\sqrt{2}}=s

Perimeter,  P=4s=(4*\frac{\sqrt{b}}{\sqrt{2}})=\frac{4\sqrt{b}}{\sqrt{2}} 
No answers match. Rationalize the denominator (get rid of the radical sign)

P=(\frac{4\sqrt{b}}{\sqrt{2}})*(\frac{\sqrt{2}}{\sqrt{2}})

P=\frac{4\sqrt{b}*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=\frac{4\sqrt{2b}}{2}=2\sqrt{2b}

Answer E

*If you do not know a square's side/diagonal relationship, use the Pythagorean theorem:
 s^2+s^2=d^2 
 2s^2=d^2 
 \sqrt{2*s^2}=\sqrt{d^2} 
 s\sqrt{2}=d

OR use 45-45-90 triangle properties. Sides opposite those angles are in the ratio of  s:s:s\sqrt{2} . 
The diagonal, opposite the 90° angle, corresponds with  s\sqrt{2} 
 s\sqrt{2}=\sqrt{b} 
 s=\frac{\sqrt{b}}{\sqrt{2}}

Pradd1984 · Answer

lets say each side is 5 so diagonal will be 5√2 or √50
perimeter will be 5x4= 20

plugin 50.

D: 2 √2(50) or 2 x 10 = 20

Answer D

If a square has a diagonal of length b, what is the perimeter of the

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If a square has a diagonal of length b, what is the perimeter of the

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