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

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New post 19 Mar 2018, 00:00
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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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Re: If a triangle of base 6 has the same area as a circle of radius 6, wha  [#permalink]

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

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New post 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.

(D) is our answer.
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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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New post 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
Hence D is the answer
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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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New post 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

Answer: D
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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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