OpenStudy (lilai3):

please help! will ward medal/fan/write testimony, etc. etc! the area of the triangle is greater than 100 square centimeters. what is the height of the triangle? estimate the height first, and then determine whether your solution is reasonable. write the inequality and explain. thank you~

OpenStudy (wolf1728):

Do you have a graphic of this?

OpenStudy (lilai3):

uhm...oh yeah oops. i forgot...sorry..my bad...|dw:1387775464301:dw|

OpenStudy (lilai3):

can you please write the inequality and explain? thanks.

OpenStudy (wolf1728):

Since there is so little information given we'll have to guess it is an equilateral triangle. area = 1/2 * base * altitude tan (60°) = alt / 4 alt = tan (60°) * 4 alt = 1.7320508076 * 4 alt = 13.8564064606 area = 1/2 * 16 * 13.8564064606 area = 8 * 13.8564064606 area = 110.8512516844 So, it passes the "area is greater than 100" test.

OpenStudy (lilai3):

what is the inequality? D:

OpenStudy (wolf1728):

I guess that would be the triangle area must be greater than 100 square cm.

OpenStudy (agent0smith):

@wolf1728 it doesn't need to be equilateral. Area is 1/2 base times height regardless. The area is >100 And area is 0.5*b*h, so \[\Large \frac{ 1 }{2}*16*h >100\]

OpenStudy (wolf1728):

agent0smith No - not for the area. But to determine the height, you need to know exactly what the angle is.

OpenStudy (agent0smith):

No, you don't... see above. We know the base, and area, that gives us one unknown - the height. Use the equation for area to find the height.

OpenStudy (lilai3):

..wait...lol you guys are making me feel confused

OpenStudy (agent0smith):

Area = 0.5bh b=16 Area = 100 Plug in and find h.

OpenStudy (lilai3):

oh wait...agent0smith you got it right.. because it's "greater than" right? oh i get it

OpenStudy (wolf1728):

h = 200/16 h = 100/8 h = 12.5

OpenStudy (lilai3):

thank you both @wolf1728 and @agent0smith !

OpenStudy (agent0smith):

\[\Large \frac{ 1 }{2}*16*h >100\]gives \[\Large h > 12.5\]

OpenStudy (lilai3):

i would like to give you both medals, but since @agent0smith is always had been helping me, and i could give him plenty of medals, i'll give this one to wolf instead..if you are okay with dat! :D

OpenStudy (wolf1728):

But it does not state definitely it is 100 cm it says estimate the height first which would be 12.5 but then they want the precise altitude

OpenStudy (the_fizicx99):

I never got my testimony ;~;

OpenStudy (lilai3):

what?

OpenStudy (the_fizicx99):

And yes @agent0smith is correct :3

OpenStudy (lilai3):

that much i got, thank you

OpenStudy (the_fizicx99):

I was talking to wolf lol >.>

OpenStudy (wolf1728):

But the answer is NOT 12.5

OpenStudy (wolf1728):

For your drawing, were you going by any instructions?

OpenStudy (lilai3):

i got 12.5.. thought, too...

OpenStudy (wolf1728):

The problem states that the area is greater than 100 sq cm. So, height is greater than 12.5 and not precisely 12.5

OpenStudy (agent0smith):

@wolf1728 that's why I used the inequality signs. h > 12.5, not h = 12.5

OpenStudy (wolf1728):

Orry, agent smith - so many conversations going on here it's hard to keep track of everything.