Question

One side of a triangle has length 6 and second length of 7 . What of the following can be the area of this triangle

I. 13
II. 21
III.24

Answer 1

none.

Answer 2

any one could be the area

Answer 3

well it has to be at least one (21) that works for a right triangle right?

Answer 4

The third side can have a length between 1 and 13. Use the http://www.algebra.com/algebra/homework/Triangles/Find-the-area-of-triangle-if-3-sides-are-given.solver page to solve ur answer. I forgot what the formula is if you were to do this on the test.

Answer 5

if the length is 13, it would be a straight line. any bigger than thirteen, it would have a large gap

Answer 6

I'm not trying to find the length of the third side. Im trying to find the possible areas of the triangle

Answer 7

sorry, hold on

Answer 8

i like 21, because if 6 is the base and 7 is the height, then 1/2 bh would be 21

Answer 9

yes, but do you think 13 of 24 would ever work?

Answer 10

hmm, let me think

Answer 11

i cant figure it out, I know that it can be 21 if it is a right triangle. sorry, I can't help more

Answer 12

13 and 21 could work. 24 could not.
We can write the equation of the area as \[A = (1/2) a b \sin \theta\] where theta is the angle between the two sides, a and b.
In this example (1/2)a*b gives 21. The sine of an angle can range from 0 to 1, so the area can range from 0 to 21.
Hence, 13 and 21 working, but not 24.

Answer 13

Weel at least the thirs side(x) must be somewhere beetween
I7-6I <x <I7+6I

Answer 14

kfujioka is correct
Area cannot be greater than 21 for a triangle with sides 6 and 7.
This occurs when angle is 90 degrees forming right triangle, thus 3rd side is sqrt(85)