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Bunuel
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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Area of Square= \(x^2\)= 5

x= \(\sqrt{5}\)

Side of Square= 3x= 3\(\sqrt{5}\)

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

Answer: B.
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Bunuel
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.

Answer: B
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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

x^2 = 5
So, (3x)^2 = 9x^2 or 9*5 = 45
Answer: B
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