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# If a triangle of base 6 has the same area as a circle of radius 6, wha

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
If a triangle of base 6 has the same area as a circle of radius 6, wha  [#permalink]

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19 Mar 2018, 00:00
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Difficulty:

15% (low)

Question Stats:

90% (00:45) correct 10% (00:51) wrong based on 48 sessions

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If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. $$6\pi$$

B. $$8\pi$$

C. $$10\pi$$

D. $$12\pi$$

E. $$14\pi$$

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Joined: 02 Sep 2009
Posts: 50009
Re: If a triangle of base 6 has the same area as a circle of radius 6, wha  [#permalink]

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19 Mar 2018, 00:01
Bunuel wrote:
If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. $$6\pi$$

B. $$8\pi$$

C. $$10\pi$$

D. $$12\pi$$

E. $$14\pi$$

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Re: If a triangle of base 6 has the same area as a circle of radius 6, wha  [#permalink]

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19 Mar 2018, 00:11
Bunuel wrote:
If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. $$6\pi$$

B. $$8\pi$$

C. $$10\pi$$

D. $$12\pi$$

E. $$14\pi$$

Area of triangle = $$0.5*b*h$$ (b is base and h is height)
Area of circle = $$\pi*R^2$$ (r is radius)

base of triangle is 6 and radius of circle is 6.

$$0.5*6*h = \pi*6^2$$
$$h = 12\pi$$

Hence option D.

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Joined: 07 Dec 2017
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Re: If a triangle of base 6 has the same area as a circle of radius 6, wha  [#permalink]

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19 Mar 2018, 01:23
Bunuel wrote:
If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. $$6\pi$$

B. $$8\pi$$

C. $$10\pi$$

D. $$12\pi$$

E. $$14\pi$$

As the required calculation is straightforward, we'll just do it.
This is a Precise approach.

Writing what we're told as an equation, b*h/2 = pi*r^2.
That is, 6h/2 = 36pi so h = 12pi.

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Re: If a triangle of base 6 has the same area as a circle of radius 6, wha  [#permalink]

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19 Mar 2018, 13:47
Area of triangle=1/2*base*Altitude= 1/2*6*Altitude =3*Altitude
Area of circle= π*r*r = π*6*6=36π

Given area of triangle= area of circle,
=>3*Altitude=36π
Altitude= 12π
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Re: If a triangle of base 6 has the same area as a circle of radius 6, wha  [#permalink]

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20 Mar 2018, 16:58
Bunuel wrote:
If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. $$6\pi$$

B. $$8\pi$$

C. $$10\pi$$

D. $$12\pi$$

E. $$14\pi$$

We can create the equation, in which h = height = altitude of the triangle. We equate the area of the triangle with base 6 to the area of the circle with radius 6:

6 x h x 1/2 = π x 6^2

3h = 36π

h = 12π

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Re: If a triangle of base 6 has the same area as a circle of radius 6, wha &nbs [#permalink] 20 Mar 2018, 16:58
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