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# If the width of a rectangle is w, the length is l, the perimeter is p,

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Math Expert
Joined: 02 Sep 2009
Posts: 51071
If the width of a rectangle is w, the length is l, the perimeter is p,  [#permalink]

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19 Aug 2018, 08:38
00:00

Difficulty:

5% (low)

Question Stats:

100% (01:23) correct 0% (00:00) wrong based on 20 sessions

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If the width of a rectangle is w, the length is l, the perimeter is p, and w = 2l, what is the area in terms of p?

(A) $$\frac{p^2}{18}$$

(B) $$\frac{p^2}{36}$$

(C) $$\frac{p}{9}$$

(D) $$\frac{p^2}{9}$$

(E) $$\frac{p}{6}$$

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Re: If the width of a rectangle is w, the length is l, the perimeter is p,  [#permalink]

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19 Aug 2018, 08:46
Bunuel wrote:
If the width of a rectangle is w, the length is l, the perimeter is p, and w = 2l, what is the area in terms of p?

(A) $$\frac{p^2}{18}$$

(B) $$\frac{p^2}{36}$$

(C) $$\frac{p}{9}$$

(D) $$\frac{p^2}{9}$$

(E) $$\frac{p}{6}$$

Area of rectangle=l*w

Perimeter, p=2(w+l)=2(2l+l)=6l or l=p/6
So, w=2l=2(p/6)=p/3

So Area= (p/6)*(p/3)=$$\frac{p^2}{18}$$

Ans. (A)
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Re: If the width of a rectangle is w, the length is l, the perimeter is p,  [#permalink]

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19 Aug 2018, 08:57
Perimeter=2 x (l+W)
p =2l+2w=W+2w(given W=2l)
p =3w=>W=p/3
Again p=3w=3x2l=6l
p=6l=> l=p/6
Area= lxw=(p/3)x (p/6)
=p^2/18
Ans A

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Re: If the width of a rectangle is w, the length is l, the perimeter is p, &nbs [#permalink] 19 Aug 2018, 08:57
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# If the width of a rectangle is w, the length is l, the perimeter is p,

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