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What is the area of the triangle?

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What is the area of the triangle?

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The figure above shows the dimensions of an isosceles triangle in terms of x. What is the area of the triangle?

(A) 24
(B) 30
(C) 48
(D) 60
(E) 96

The OA is C.

I need to find the value of x, I think that I can do it of the following way, as I have 2 right triangles I can use Pithagoras theorem and get the value of x, right? Then with it I can determine the area of the triangle.

Please, can any expert explain this PS question for me? I tried to solve it of this way but I can't get the correct answer. I need your help. Thanks.

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Quote:
The figure above shows the dimensions of an isosceles triangle in terms of x. What is the area of the triangle?

(A) 24
(B) 30
(C) 48
(D) 60
(E) 96

The OA is C.
Hi Swerve,
Let's take a look at your question.

Since the given triangle is an isosceles triangle, therefore, two of the sides of the triangle are congruent.
We can see that the base angles are the same i.e. y degrees, hence sides opposite to these two angles will be the same in length.
Therefore,
$$2x-2=3x-8$$
$$3x-2x=8-2$$
$$x=6$$

Now we can find the area of the triangle using the formula:
$$\text{Area of Triangle}=\frac{1}{2}\left(Base\right)\left(Height\right)$$
$$\text{Area of Triangle}=\frac{1}{2}\left(3x-2\right)\left(x\right)$$
Substitute x = 6, we get,
$$\text{Area of Triangle}=\frac{1}{2}\left[3\left(6\right)-2\right]\left(6\right)$$
$$\text{Area of Triangle}=\frac{1}{2}\left[18-2\right]\left(6\right)$$
$$\text{Area of Triangle}=\frac{1}{2}\left[16\right]\left(6\right)$$
$$\text{Area of Triangle}=8\left(6\right)=48$$

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.

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Hi swerve,

We're told that the large triangle is an ISOSCELES triangle. We're asked to find the area of the triangle. While there are lengthy 'math' approaches to answering this question, you can use the relationship of the sides and do a bit of basic arithmetic to get to the correct answer.

To start, it's worth noting that the large triangle is ISOSCELES, so (2X - 2) and (3X - 8) MUST end up equaling the same value. Thus, we can set them equal to one another:

2X - 2 = 3X - 8
6 = X

Area of the big triangle = (1/2)(X)(3X - 2) =
(1/2)(6)(16) =
(1/2)(96) =
48

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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