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# If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of  [#permalink]

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07 Feb 2019, 01:51
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Difficulty:

45% (medium)

Question Stats:

65% (01:29) correct 35% (01:56) wrong based on 17 sessions

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If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of the circle, in terms of x, is

A. $$\sqrt{3} x\pi$$

B. $$\sqrt{5} x\pi$$

C. $$\sqrt{3x} \pi$$

D. $$\sqrt{5x} \pi$$

E. $$5x^2 \pi$$

Attachment:

Geometry_015.jpg [ 8.72 KiB | Viewed 288 times ]

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Re: If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of  [#permalink]

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07 Feb 2019, 02:09
Bunuel wrote:

If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of the circle, in terms of x, is

A. $$\sqrt{3} x\pi$$

B. $$\sqrt{5} x\pi$$

C. $$\sqrt{3x} \pi$$

D. $$\sqrt{5x} \pi$$

E. $$5x^2 \pi$$

If ABCD is a rectangle, lets calculate AC

AC =$$\sqrt{{x^2 + 4* x^2}}$$
AC = $$\sqrt{5}$$x

AC will be the diameter, radius will be $$\sqrt{5}$$x / 2

C = 2 $$\pi r$$
= 2 * $$\pi$$$$\sqrt{5}$$x / 2
= $$\sqrt{5} x\pi$$
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Re: If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of  [#permalink]

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07 Feb 2019, 02:12
Attachment:

image.jpg [ 28.22 KiB | Viewed 177 times ]

From the above fig, the diagonal of the rectangle serves as the diameter of the circle as the diagonal passes through the center of both the circle and the rectangle.

Since the diameter is of $$\sqrt{5}x$$, radius of the circle $$\frac{\sqrt{5}x}{2}$$

The circumference of a circle is $$2\pi r$$ = $$2*\pi*\frac{\sqrt{5}x}{2}$$

$$\sqrt{5}x \pi$$

OPTION: B
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Re: If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of  [#permalink]

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07 Feb 2019, 02:52
diaganol of the rectangle = diameter of circle
d of rectangle = \sqrt{5}x

2 * pi * \sqrt{5}x/2

=>$$\sqrt{5} x\pi$$
IMO B

Bunuel wrote:

If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of the circle, in terms of x, is

A. $$\sqrt{3} x\pi$$

B. $$\sqrt{5} x\pi$$

C. $$\sqrt{3x} \pi$$

D. $$\sqrt{5x} \pi$$

E. $$5x^2 \pi$$

Attachment:
Geometry_015.jpg

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Re: If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of   [#permalink] 07 Feb 2019, 02:52
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