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What is the area of the triangle ABC?

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What is the area of the triangle ABC?  [#permalink]

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New post 15 Mar 2018, 11:54
2
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

35% (01:57) correct 65% (01:33) wrong based on 41 sessions

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What is the area of the triangle ABC?
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1)\(y^2\)-14y+48=0
2) \(y^2\)-16y+60=0

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What is the area of the triangle ABC?  [#permalink]

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New post 15 Mar 2018, 12:38
1
Using Hero's formula
Area = \(\sqrt{s(s-a)(s-b)(s-c)}\) where s = \(\frac{a+b+c}{2}\)

1)\(y^2\)-14y+48=0

On simplifying this equation
we get \(y^2 - 6y - 8y + 48 = 0\) -> \(y(y-6) - 8(y-6) = 0\) -> \((y-6)(y-8) = 0\)
Therefore, y could take the values 6 or 8.

For both the values of y for triangle ABC, the Area is 12. (Sufficient)

2) \(y^2\)-16y+60=0

On simplifying this equation,
we get \(y^2 - 10y - 6y + 60 = 0\) -> \(y(y-10) - 6(y-10) = 0\) -> \((y-6)(y-10) = 0\)
Therefore, y could take the values 6 or 10

A triangle with y = 10 is not possible.

The Area of Triangle ABC with sides a=b=5 and c=6 is 12. (Sufficient - Option D)
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What is the area of the triangle ABC? &nbs [#permalink] 15 Mar 2018, 12:38
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