Geometry Question Bank #3

[cssears]

In the geometry question bank the third question is "The (x, y) coordinates of points P and Qare (-2, 9) and (-7, -3), respectively. The height of equilateral triangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?"

In strategy Guide 5 page 34 it states the area of an equilateral triangle with the side length of S is equal to S^2 (root 3) / 4. Following this formula I this equation results:

26^2 (root 3) / 4 this simplifys to 676 (root 3) / 4 then simplifies to 169 root 3.

The question bank says the answer is 169 (root 3) / 3. The question bank solution also does not use the formula provided on page 34 of strat guide 5.

What am I missing here?

[ps63739]

The question says height is distance between two points.
Now height of triangle = length between two points = 13.

13 is the height. Side of the triangle will be 13/sin60 = 13x2/sqrt(3)

Now - use formula Area of triangle = sqrt(3)/4 * side*side
sqrt(3) * 169*4 /3

[thoppae.saravanan]

Hi cssears,

You have calculated the length of line segment incorrectly. It should be 13. If you work out with this value, you will get the right answer.

[deem432]

I don't understand why the answer to this question is not 169 (sqrt3) / 4.

Will someone please explain this to me? I am confused.

[RonPurewal]

hi,
please re-post this query in the MGMAT non-CAT math folder.

thanks.