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

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
A triangle and a circle have equal areas. If the base of the triangle  [#permalink]

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10 Jan 2019, 01:47
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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

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

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10 Jan 2019, 01:54
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

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

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10 Jan 2019, 05:39

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

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

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10 Jan 2019, 06:11
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 &nbs [#permalink] 10 Jan 2019, 06:11
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