what's the TRIANGLE area and perimeter of a right triangle

Question

hypotenuse = (2x - 4)

bottom side = 6

left side = (x+3)

Answer 1

(2x-4)² = (x+3)² +6²

hypotenuse squared = sum of squares of the other two sides

expand to get

4x² -16x +16 = x² + 6x + 9 + 36

3x² -22x -29 = 0

can't factor, so try completing the square

x² -22x/3 -29/3 = 0

(x - 11/3)² = 29/3 +121/9 = 208/9

x- 11/3 = (208)^1/2/3

x = slightly more than 14/3 +11/3 = 25/3 = slightly more than 8, maybe 8.5

Now plug this x value back into the original sides of the triangle:

2x-4 = 2(8.5)-4= 17- 4= about 13

x+3 = 8.5+3 = 11.5

other side is 6

Area is 1/2 height times base or 6 times 11.5 =69/2 = 34.5

Perimeter is the sum of all 3 sides:

6+11.5+13= 30.5

Approximately

check to see if the sides satisfy the theorem:

hypotenuse squared = sum of other sides squared.

13 squared = 169= 132.25 + 36 = 168.25 close enough