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# What is the area of a rectangle whose length is twice its width and wh

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Joined: 02 Sep 2009
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What is the area of a rectangle whose length is twice its width and wh  [#permalink]

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31 Jan 2019, 21:04
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Difficulty:

25% (medium)

Question Stats:

76% (01:35) correct 24% (01:47) wrong based on 23 sessions

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What is the area of a rectangle whose length is twice its width and whose perimeter is equal to that of a square whose area is 1?

A) $$1$$

B) $$6$$

C) $$\frac{2}{3}$$

D) $$\frac{4}{3}$$

E) $$\frac{8}{9}$$

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Re: What is the area of a rectangle whose length is twice its width and wh  [#permalink]

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31 Jan 2019, 22:53
Bunuel wrote:
What is the area of a rectangle whose length is twice its width and whose perimeter is equal to that of a square whose area is 1?

A) $$1$$

B) $$6$$

C) $$\frac{2}{3}$$

D) $$\frac{4}{3}$$

E) $$\frac{8}{9}$$

l = 2*w

Perimeter of the rectangle $$= 2*(l+w) = 4*1$$ (Side of square with area 1 will be 1)

i.e. $$(l+w) = 2$$

i.e. $$2w+w = 3w = 2$$

i.e. $$w = 2/3$$ and $$l = 4/3$$

Area of rectangle $$= l*w = (2/3)*(4/3) = 8/9$$

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Re: What is the area of a rectangle whose length is twice its width and wh  [#permalink]

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01 Feb 2019, 09:57
Bunuel wrote:
What is the area of a rectangle whose length is twice its width and whose perimeter is equal to that of a square whose area is 1?

A) $$1$$

B) $$6$$

C) $$\frac{2}{3}$$

D) $$\frac{4}{3}$$

E) $$\frac{8}{9}$$

l=2w
2*( l+w)= 4
6w=4
w=2/3
l=4/3
l*w= 8/9
IMO E
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What is the area of a rectangle whose length is twice its width and wh  [#permalink]

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03 Feb 2019, 17:30
Bunuel wrote:
What is the area of a rectangle whose length is twice its width and whose perimeter is equal to that of a square whose area is 1?

A) $$1$$

B) $$6$$

C) $$\frac{2}{3}$$

D) $$\frac{4}{3}$$

E) $$\frac{8}{9}$$

This problem just requires meticulousness.

(1) area of square = 1
gives side length, $$s$$

Area of square = $$1=s^2$$
$$\sqrt{1}=\sqrt{s^2}$$
$$s=1$$

(2) Perimeter of square =
$$4s=(4*1)=4=$$
perimeter of rectangle

Use rectangle perimeter to find side lengths of rectangle.
From side lengths, find area.

(3) Perimeter of rectangle: side lengths?

Perimeter, $$P=4$$
$$2l+2w=P$$
$$2l+2w=4$$
$$2(l+w)=4$$ - (divide by 2)
$$(l+w)=2$$

The length of the rectangle is twice its width

$$l=2w$$
Substitute $$2w$$ for $$l$$

$$(l+w)=2$$
$$2w+w=2$$
$$3w=2$$
$$w=\frac{2}{3}$$
$$l=2w=(2*\frac{2}{3})=\frac{4}{3}$$

(4) Area, A, of rectangle?
$$A=l*w$$

$$A=(\frac{4}{3}*\frac{2}{3})=\frac{8}{9}$$

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What is the area of a rectangle whose length is twice its width and wh   [#permalink] 03 Feb 2019, 17:30
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