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A square playground has the same area as a rectangular playground that
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Bunuel
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A square playground has the same area as a rectangular playground that [#permalink] New post  31 Oct 2015, 04:37
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A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

(A) \(10\sqrt{5}\)
(B) \(10\sqrt{6}\)
(C) 25
(D) 50
(E) 60
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anudeep133
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Re: A square playground has the same area as a rectangular playground that [#permalink] New post  31 Oct 2015, 05:01
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Bunuel wrote:
A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

(A) \(10\sqrt{5}\)
(B) \(10\sqrt{6}\)
(C) 25
(D) 50
(E) 60


Solution: \(a^{2} = (a+30)(a-20) ==> 10a=600 ==> a=60\)

Option E
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kbangia
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Re: A square playground has the same area as a rectangular playground that [#permalink] New post  31 Oct 2015, 05:52
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Bunuel wrote:
A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

(A) \(10\sqrt{5}\)
(B) \(10\sqrt{6}\)
(C) 25
(D) 50
(E) 60



Fairly Simple.

x= Side of Square Playground
and cause it says the Area is the same

\(X^2\)=the area of the Square Playground

Now,
The rectangle sides are \(x+30 and x-20\)

Therefore the Area of the rectangle will be \(x+30 X x-20\)


Considering area of the two are the same\(x^2=x+30 X x-20\)

Solve for \(x\)
\(10x=600\)
\(x=60\)
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kbangia
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Re: A square playground has the same area as a rectangular playground that [#permalink] New post  31 Oct 2015, 05:55
Bunuel wrote:
A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

(A) \(10\sqrt{5}\)
(B) \(10\sqrt{6}\)
(C) 25
(D) 50
(E) 60



Fairly Simple.

Square:

\(x=\) Side of Square Playground
and cause it says the Area is the same

\(x^2\)=the area of the Square Playground

Rectangle:

The rectangle sides are \(x+30\) and \(x-20\)

Therefore the Area of the rectangle will be \(x+30 X x-20\)

Area:
Considering area of the two are the same\(x^2=x+30 X x-20\)

Solve for \(x\)
\(10x=600\)
\(x=60\)

Side of the square is 60
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keats
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A square playground has the same area as a rectangular playground that [#permalink] New post  31 Oct 2015, 11:02
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A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

___________________

Let the side of the square be 'a' and that of rectangle be l (length) and b (breadth)
l = a+30
b = a-20
a^2 = (a+30) (a-20)
a^2 = a^2 +10a -600
a=60
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Abhishek009
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Re: A square playground has the same area as a rectangular playground that [#permalink] New post  25 Nov 2016, 08:12
Bunuel wrote:
A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

(A) \(10\sqrt{5}\)
(B) \(10\sqrt{6}\)
(C) 25
(D) 50
(E) 60

\(a^2 = ( a + 30 ) ( a - 20 )\)

Or, \(a^2 = a^2+10a−600\)

Or, \(10a = 600\)

So, \(a = 60\)

Answer will be (E) 60
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