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Triangle STV has sides...

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by AAPL » Thu Jan 11, 2018 3:05 pm
Triangle STV has sides ST = TV = 17, and SV = 16. What is the area?

(A) 85
(B) 100
(C) 120
(D) 136
(E) 165

The OA is C.

I don't have clear this PS question, I know that its an isosceles triangle but can I say that SV is it base? then I can get its height using Pythagoras Theorem?
$$Height\ =\ \sqrt{17^2-8^2}$$
Finally, I can get the area of the triangle.
$$A_{\triangle}\ =\ \frac{1}{2}b\cdot h$$
I appreciate if any expert explain it for me. Thank you so much.
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by GMATWisdom » Fri Jan 12, 2018 7:05 am
AAPL wrote:Triangle STV has sides ST = TV = 17, and SV = 16. What is the area?

(A) 85
(B) 100
(C) 120
(D) 136
(E) 165

The OA is C.

I don't have clear this PS question, I know that its an isosceles triangle but can I say that SV is it base? then I can get its height using Pythagoras Theorem?
$$Height\ =\ \sqrt{17^2-8^2}$$
Finally, I can get the area of the triangle.
$$A_{\triangle}\ =\ \frac{1}{2}b\cdot h$$
I appreciate if any expert explain it for me. Thank you so much.
For calculating area of an isosceles triangle, it is easier to take unequal side as the base. Thus, it’s the right choice to take SV as the base. Then if we join common point T of equal sides to the midpoint of SV by a line then that line would be perpendicular to the base SV. Then you can find the height using the Pythagoras formula and calculate the area of the triangle as below:
Height=√(17^2-8^2) =√225=15
Area=(1/2)*16*15=120
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by [email protected] » Fri Jan 12, 2018 11:20 am
Hi AAPL,

We're told that triangle STV has sides ST = TV = 17, and SV = 16. We're asked for the area of this triangle. While this prompt may appear a bit tricky, the wording of the prompt (and the answer choices) gives us a way to get to the correct answer without doing too much complex math...

To start, you might find it helpful to draw the triangle (it's ISOSCELES - with a base of 16 and two 'diagonals' of 17 each). To figure out the area of a triangle, we'll use the triangle area formula:

Area = (1/2)(Base)(Height)

We already know that the base of this triangle is 16... so the answer to this question is (1/2)(16)(Height) = 8(Height).

Notice how the question asks for the 'area'.... NOT the 'approximate area'... and that all of the answers are INTEGERS. This makes it HIGHLY likely that the Height of this triangle is an INTEGER and that the correct answer is a MULTIPLE of 8 (since the area is 8 times 'something'). The two diagonals are 17, so the height of the triangle MUST be LESS than 17.

IF... the height was 17 (which again - it's not - it's LESS than 17), then the area would be 8(17) = 136. This area is TOO BIG though. We need an answer that is a bit less than 136 and a multiple of 8. There's only one answer that matches.

Final Answer: C

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