Which of the following statements individually provide(s) sufficient

Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle ABC above? Indicate all such statements. DBC is an equilateral triangle., ABD is an isosceles triangle., The length of BC is equal to the length of AD., The length of BC is 10., The length of AD is 10.

3 Explanations

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Malak Kudaimi

I'm not sure I understand why it's necessary to move the the triangle around to create other possible combinations? What if you're not creative and can't think that way, especially in a time crunch? It would've taken me years to figure out those possible combinations in the explanation video. Isn't there a simpler way to solve this problem using the triangle that's already drawn? For example, with answer C, It it tells you that BC is equal to AD, this means that you know the length of BC, meaning you have all you need to solve for the area.

Aug 5, 2017 • Comment

Jonathan , Magoosh Tutor

Hi Malak,
This is a difficult question that is precisely testing our ability to evaluate information and think creatively.

We know ADC is a right angle and we know the value of AD. If we know BC we can find the triangle area. So the question we're thinking of is: is there only one possible length of BC based on this information?

Given we are trying to answer the question of whether BC is fixed, it should make sense to try to create different lengths of BC based on the information.

Rather than thinking of different possibilities for the equilateral triangle first, we could just draw two different lengths BC and see whether we can make ABD isosceles. We can --- so that means (B) isn't sufficient.

Please note that (C) also isn't sufficient. We can make two different lengths BC and we can still just draw AD to be equal to BC.

To recap, if we know BC we know the area. So for each piece of information, we want to see whether more than one length for BC is possible. Perhaps this way is more intuitive?

I hope that helps.

Sep 4, 2017 • Reply

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Jacob Elder

Could you elaborate further on why (B) knowing ABD is an isosceles triangle is wrong? I'm not sure I understood the explanation in the video. It was explained that knowing DBC is an equilateral triangle is helpful because then we can use the ratio for equilaterals to determine the area. Can't we do the same for isosceles triangles?

Jan 24, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

The key here is the ability to "manipulate" ABD, given that this triangle is isosceles. Whereas an equilateral triangle has three congruent angles of 60?, in an isosceles triangle, we can change the angle measurements, as long as two of the three angles are of equal measure. This allows us to draw different possibilities for ABD. We are able to maintain the 90? angle, as well as the length of AB. However, and as Chris shows, by changing the angle measurements of ABD, the length of side BC and the height of triangle ABC are changed. Because of this, we cannot determine the area of ABC given the fact that ABD is an isosceles triangle.

I hope this helps clear up your doubts!

Jan 26, 2016 • Reply

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Chris Lele