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# If the area of a square of side x is 5, what is the area of a square

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Math Expert
Joined: 02 Sep 2009
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If the area of a square of side x is 5, what is the area of a square  [#permalink]

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08 Mar 2018, 01:16
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25% (medium)

Question Stats:

75% (00:30) correct 25% (00:40) wrong based on 48 sessions

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If the area of a square of side x is 5, what is the area of a square of side 3x?

(A) 15

(B) 45

(C) 95

(D) 75

(E) 225

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Joined: 02 Sep 2009
Posts: 50714
Re: If the area of a square of side x is 5, what is the area of a square  [#permalink]

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08 Mar 2018, 01:17
Bunuel wrote:
If the area of a square of side x is 5, what is the area of a square of side 3x?

(A) 15

(B) 45

(C) 95

(D) 75

(E) 225

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Re: If the area of a square of side x is 5, what is the area of a square  [#permalink]

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08 Mar 2018, 04:25
Bunuel wrote:
If the area of a square of side x is 5, what is the area of a square of side 3x?

(A) 15

(B) 45

(C) 95

(D) 75

(E) 225

Area of square = side^2

i.e. $$x^2 = 5$$

Area of the square with side 3x = $$(3x)^2= 9x^2 = 9*5 = 45$$

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Re: If the area of a square of side x is 5, what is the area of a square  [#permalink]

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08 Mar 2018, 23:44
Bunuel wrote:
If the area of a square of side x is 5, what is the area of a square of side 3x?

(A) 15

(B) 45

(C) 95

(D) 75

(E) 225

IMO B area of square is side^2 so x^2=5 then x=root 5
3x=3root5
area of new square is 3x^2
3root5^2
=9*5=45
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Re: If the area of a square of side x is 5, what is the area of a square  [#permalink]

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09 Mar 2018, 19:48
Area of Square= $$x^2$$= 5

x= $$\sqrt{5}$$

Side of Square= 3x= 3$$\sqrt{5}$$

Area= $$(3\sqrt{5})^2$$= 45

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Re: If the area of a square of side x is 5, what is the area of a square  [#permalink]

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12 Mar 2018, 09:06
Bunuel wrote:
If the area of a square of side x is 5, what is the area of a square of side 3x?

(A) 15

(B) 45

(C) 95

(D) 75

(E) 225

We see that x^2 = 5, so x = √5.

Thus, 3x = 3√5, so the area of a side of 3x is (3√5)^2 = 9 x 5 = 45.

Alternate solution:

If a side of a square is increased by a factor of m, then its area is increased by a factor of m^2. Here, the side of the square is increased by a factor of 3, so the area will be increased by a factor of 3^2 = 9. Thus, the area of the square in question is 5 x 9 = 45.

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Re: If the area of a square of side x is 5, what is the area of a square &nbs [#permalink] 12 Mar 2018, 09:06
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