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Re: The area of a triangle with sides 6, 8, and 10 [#permalink]
Answer: B
A: The area of a triangle with sides 6, 8, 10
By this information we can deduce that it is a right side traingle (6^2 + 8^2 = 10^2)
So it’s area equals: 6 * 8 / 2 = 24

B: The area of an equilateral triangle with side 8.
We know the base of triangle is 8, for calculating it’s area we need to know it’s height. If we draw the shape we will see:
h^2 + (8/2)^2 = 8^2 ->
h^2 = 64 - 16 = 48 ->
h = √48 = 4√3
Area = 1/2 * h* base = 1/2 * 4√3 * 8 = 16√3

Now we need to compare 24 and 16√3, Which 16√3 is bigger. The answer is B

** In general height of a equilateral traingle which it’s sides are “a", is √3*a/2
h^2 + (a/2)^2 = a^2 ->
h^2 = a^2 - a^2/4 ->
h^2 = 3a^2/4
h = √3*a/2
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Re: The area of a triangle with sides 6, 8, and 10 [#permalink]
1
I was confused by A!
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The area of a triangle with sides 6, 8, and 10 [#permalink]
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Carcass wrote:
Quantity A
Quantity B
The area of a triangle with sides 6, 8, and 10
The area of an equilateral triangle with side 8


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Col. A: \(\frac{1}{2}(6)(8) = 24\)
Col. B: \(\frac{\sqrt{3}}{4}(8^2) = 16\sqrt{3}\)

Dividing by \(16\) both sides;

Col. A: \(1.5\)
Col. B: \(1.73\)

Hence, option B
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Re: The area of a triangle with sides 6, 8, and 10 [#permalink]
QA don't state that 6,8,10 is right angle triangle? it can be scalen triangle....
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Re: The area of a triangle with sides 6, 8, and 10 [#permalink]
void wrote:
QA don't state that 6,8,10 is right angle triangle? it can be scalen triangle....


Even if doesn't say it is a right triangle, but it will always be!

Apply Cosine rule:

Angle C (opposite to side 10) = \(Cos^-1 [\frac{6^2 + 8^2 - 10^2}{(2)(6)(8)}]\)

C = \(Cos^-1 [\frac{0}{90}]\)

C = \(Cos^-1 (0) = 90\)
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Re: The area of a triangle with sides 6, 8, and 10 [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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