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

Question

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}

PKN · Answer

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)

BARUAH · Answer

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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jahongirnorimov · Answer

This question can be solved either with smart numbers or algebra. First, consider plugging in smart numbers.
Set l = 2, so w = 4. The perimeter will be 2l + 2w = 2(2) + 2(4) = 12. The answer is the area, which is wl = (2)(4) = 8
based on these numbers. Now plug p = 12 into the choices to see which choice equals 8:
(A) 144/18 = 8
(B) 144/36 = 4
(C) 12/9 = 4/3
(D) 144/9 = 16
(E) 12/6 = 2
The correct answer is (A).

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

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

Prep Toolkit

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