This question is from the mini quiz of the day- June 24

Why can’t the height be 5? Why only 7 or 9?

hypotenuse will be 11.40. base will be 5 . so according to rule 2 sides need will be greater than third side.

if we 5+5 will <11 so, third size need to be > 7

I was really confused by that, this is what I thought would be the case:

There are 3 bases in a triangle, so there can be 3 possible heights:

(All the sides are calculated using the distance formula)

Case II is the easiest:

h2 = x coordinate of the (7,9) point = 7

For case I:

The area of the triangle will be the same no matter which base, height set we choose, so:

1/2 x b1 x h1 = 1/2 x b2 x h2

11.4 x h1 = 5 x 7

h1 = 35/11.4 = 3.07

For case III as well:

The area of the triangle will be the same no matter which base, height set we choose, so:

1/2 x b3 x h3 = 1/2 x b2 x h2

8.1 x h3 = 5 x 7

h3 = 35/8.1 = 4.32

So, all the 3 heights would be (7, 3.07, 4.32)

Not sure how 9 works???

Hope @gregmat can clear this up.

1 Like

Correct! Good find! I should have said “find the OBVIOUS heights” haha.

Wouldn’t that only be 7 then, how does the 9 work?

Was going to respond - @vidishas is right. The question is ambiguous. There really isn’t an “obvious” height - what should be given is the corresponding base.

Obvious as in look at the x and y coordinate

Thanks so much!