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A triangle and a circle have equal areas. If the base of the triangle

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A triangle and a circle have equal areas. If the base of the triangle  [#permalink]

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New post 10 Jan 2019, 02:47
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:07) correct 25% (01:31) wrong based on 14 sessions

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A triangle and a circle have equal areas. If the base of the triangle  [#permalink]

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New post 10 Jan 2019, 02:54
The answer is B
Radius of circle is 5/2
The area of Circle is Pi(r)^2 ie 25/4pi
Area of triangle = 1/2*B*h
base =5
Solving for h = 5(pi)/2

Please post the official answer.

Please explain if my answer is incorrect..
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Re: A triangle and a circle have equal areas. If the base of the triangle  [#permalink]

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New post 10 Jan 2019, 06:39

Solution


Given:
    • A triangle and a circle have equal areas
    • Base of the triangle = 5
    • Diameter of the circle = 5

To find:
    • The height of the triangle

Approach and Working:
    • Area of circle = \(ᴨr^2 = ᴨ(\frac{5}{2})^2 = \frac{25ᴨ}{4}\)
    • Area of triangle = \(\frac{1}{2} * b * h = \frac{1}{2} * 5 * h\)
    • Thus, \(\frac{5h}{2} = \frac{25ᴨ}{4}\)

Therefore, \(h = \frac{5ᴨ}{2}\)

Hence, the correct answer is Option B

Answer: B

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Re: A triangle and a circle have equal areas. If the base of the triangle  [#permalink]

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New post 10 Jan 2019, 07:11
Bunuel wrote:
A triangle and a circle have equal areas. If the base of the triangle and the diameter of the circle each have length 5, what is the height of the triangle?

A. 5/2

B. \(\frac{5\pi}{2}\)

C. \(5\pi\)

D. \(10\pi\)

E. It cannot be determined from the information given



1/2 * b*h = pi * r2
1/2 * 5*h= pi * 5/2 * 5/2
h = 5 Pi/2 IMO B
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Re: A triangle and a circle have equal areas. If the base of the triangle   [#permalink] 10 Jan 2019, 07:11
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