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# A square playground has the same area as a rectangular playground that

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Math Expert
Joined: 02 Sep 2009
Posts: 50002
A square playground has the same area as a rectangular playground that  [#permalink]

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31 Oct 2015, 05:37
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:34) correct 29% (01:23) wrong based on 161 sessions

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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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Joined: 10 Aug 2015
Posts: 103
Re: A square playground has the same area as a rectangular playground that  [#permalink]

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31 Oct 2015, 06:01
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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Joined: 17 Feb 2014
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Re: A square playground has the same area as a rectangular playground that  [#permalink]

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31 Oct 2015, 06:52
1
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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Joined: 17 Feb 2014
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Re: A square playground has the same area as a rectangular playground that  [#permalink]

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31 Oct 2015, 06:55
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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A square playground has the same area as a rectangular playground that  [#permalink]

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31 Oct 2015, 12:02
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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Re: A square playground has the same area as a rectangular playground that  [#permalink]

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25 Nov 2016, 09:12
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, $$a = 60$$

_________________

Thanks and Regards

Abhishek....

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Re: A square playground has the same area as a rectangular playground that  [#permalink]

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12 Mar 2018, 23:00
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