The altitude and the median from the same vertex of a triangle trisect the angle. find the area of the triangle, if the length of the shorter side is 4√ 3 in.

  24√3 in²

Step-by-step explanation:

The triangle in question is a 30°-60°-90° right triangle. Such triangles have side lengths in the ratio ...

  1 : √3 : 2

Given that the short side has length 4√3, the side at right angles to it will have length (4√3)(√3) = 12. Then the area is ...

  A = 1/2bh = 1/2(4√3)(12) = 24√3 . . . square inches

_____

If you make the assumption that the triangle is a right triangle, and the angle being trisected is the right angle, then you find that assumption is true. If you work through the algebra and geometry, you can prove this is the only possible such triangle. That proof is beyond the scope of this answer.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

the answer to this question is 3/19

step-by-step explanation: