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# What is the area of the triangle ABC?

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Manager
Joined: 03 Mar 2018
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What is the area of the triangle ABC?  [#permalink]

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15 Mar 2018, 10:54
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2
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Difficulty:

85% (hard)

Question Stats:

33% (01:57) correct 67% (01:31) wrong based on 42 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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15 Mar 2018, 11:38
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, 11:38
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