Answer:
There are no points for C to make this triangle
Step-by-step explanation:
We need to find the distance from point A to B
d = sqrt((x2-x1)^2 + (y2-y1)^2 )
= sqrt((5-1)^2 + (5-2)^2
= sqrt(4^2 + 3^2)
= sqrt(16+9)
= sqrt(25)
= 5
We know the hypotenuse only
We can find the base in terms of the hypotenuse using the Pythagorean theorem
c^2 = a^2 + b^2
c^2 - a^2 = b^2
Taking the square root of each side
sqrt( c^2 - a^2) = sqrt(b^2)
sqrt( c^2 - a^2) = b
c = 5
sqrt(25 - a^2)=b
The area of a triangle is
A = 1/2 b* h where b is the base and a is the height
6.5 = 1/2 (sqrt(25-a^2)) *a
Multiply each side by 2
2*6.5 = 2*1/2 (sqrt(25-a^2)) *a
13 = (sqrt(25-a^2)) *a
Divide each side by a
13/a = sqrt(25-a^2)
Square each side
169/a^2 = 25-a^2
Multiply each side by a^2
169 = 25a^2 -a^4
Subtract 169 from each side
0= -a^4 +25a^2 -169
Divide by -1
0= a^4 -25a^2 +169
Using the discriminant
b^2 -4ac
25^2 - 4 * 1 * 169
625 - 676
-51
a^2 is imaginary
There is no solution
