Possible area of a triangle?

Question

what is the greatest possible area of a triangle with one side of length 7 and another side length of 10?
a.17
b.34
c.35
d.70
e.140

and why?

Answer 1

Since the area of a triangle is base x height, the maximum area would be achieved with a right triangle. If you choose either of the sides as the base, placing the other known side at right angles to the base will produce the maximum height.

Answer 2

Let the base of your triangle be 10 (I could use 7, but 10 is evenly divisible by 2.)
The area of any triangle is (1/2)bh.
(1/2)(10)h = 5h
h for this triangle can never exceed 7, which is its value when the 7 is perpendicular to the 10, so the maximum area of this triangle must be 5*7 = 35

Answer 3

If it's a right triangle, the area is 35: base times perpendicular height, divided by 2.

If it's not, then a lot more math is needed to figure it out.

Answer 4

c.35

dunno, something along the line of 7 x 10 = 70
70 divide 2 = 35

Answer 5

A because the other side can not have a side better than the rest the of the triangle.

Answer 6

c. 35. A right triangle would give you the greatest area.

Answer 7

c. 35 because you multiply 10*7 and get 70 but when you are trying to find the area you have to take half so you divide by 2 and you get 35.

35+35=70
70/2=35
remeber to take half and thats how you get your answer.

Answer 8

Since A = ½bh and h = Lsinα, for max area α must be 90°
Ergo, c. is correct

Answer 9

idk d because i like 70 and im not good at math
srry thats my answer and im stickin to it