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When the length of each side of a square is tripled, the area of the

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Bunuel
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When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 01:56
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89% (01:16) correct 11% (01:47) wrong based on 74 sessions
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When the length of each side of a square is tripled, the area of the new square is 200 more square inches than the area of the original square. What is the length, in inches, of each side of the original square?

A. 4
B. 5
C. 10
D. 15
E. 20
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B
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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 02:19
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Solution


    • Let us assume that each side of the original square is a inch.
      o Area of the original square \(= a^2\) square inches
      o Each side of the new square \(= 3a\) inches
         Area of the new square \(= (3a)^2 = 9a^2\) square inches.
    • Now, the area of the new square is 200 more square inches than the area of the original square.
      o This means, \(9a^2 = a^2 + 200\)
      \(⟹ 8a^2 = 200\)
      \(⟹ a^2 = 25\)
      \(⟹ a = 5\) inches
Thus, the correct answer is Option B.
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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 02:19
Explanation:

Let the side of original square is x, then other one will have 3x

(3x)^2 - x^2 = 200
8x^2 = 200
x^2 = 25
x = 5

IMO-B
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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 02:22
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Side of original square = a
=> Area of original square = a^2

Side of new square = 3a
=> Area of new square = 9a^2

Now,
9a^2 - a^2 = 200
=> 8a^2 = 200
=> a^2 = 25
=> a = 5

Answer: B

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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 03:09
IMO-B

Given
Side of original square-l
Side of new square. -3l

Difference in area of new square and original square is -200
Area of square=l^2

200=(3l)^2-l^2
200=8l^2
l= 5 answer

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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 03:42
Kindly see the attachment.

Time: 1:09

The solution contains only the steps I took during exam mode for this question.
IMO B
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1.jpeg [ 19.55 KiB | Viewed 2118 times ]

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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 04:54
Original side be x
Original area is x^2
New side is 3x and new area is 9x^2
New area = original area+ 200 sq inch

9x^2 = x^2 + 200
X is 5

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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 06:37
Let original side of square be s.
According to question, Side is tripled,
\(3s * 3s = s^2 + 200\)
=> \(9s^2 = s^2 + 200\)
=> \(8s^2 = 200\)
=> \(s^2 = 25\)
=> \(s = 5\)
As side can't be negative.

Thus OA is B
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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 07:08
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Let the length of each side of square is x
if we consider 4^2=16 as length, then increase length 12^2 is 144 , so increase length must be greater than 4
area of square = side^2

15^2 - 5^2 = 200
225-25=200


ANS=B
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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 07:33
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IMO B

Ratio of area = Initial Area / Final Area = x^2 / (3x)^2 = 1/9
A/Q, Let Initial area = K , Final Area = 9K
9K-K= 200
K= 200/8 = 100/4 = 25

K = (Side)^2 = 25
Side = 5 unit

B. 5
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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 08:36
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Ans - B

Original length L, area = L^2
New length 3L, new area= (3L)^2= 9L^2

New A = A + 200
9L^2- L^2 = 200

L=5

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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 11:40
Answer B - 5
3a^2-a^2=200
a^2=25
a=5
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Re: When the length of each side of a square is tripled, the area of the [#permalink] When the length of each side of a square is tripled, the area of the   30 Jun 2020, 21:57
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When the length of each side of a square is tripled, the area of the new square is 200 more square inches than the area of the original square. What is the length, in inches, of each side of the original square?

A. 4
B. 5
C. 10
D. 15
E. 20

old new
length a 3a
area a^2 9a^2

9a^2=a^2+200
on solving.,
a=5

Ans B
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Re: When the length of each side of a square is tripled, the area of the [#permalink]
30 Jun 2020, 21:57
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