9514 1404 393
Answer:
in the order (5m, 3m, 2m+2), ...
- 5, 3, 4
- (2+√34)/3, (2+√34)/5, (34+2√34)/15 ≈ (2.6103, 1.5662, 3.0441)
Step-by-step explanation:
There are two possible solutions:
<u>5m is the hypotenuse</u>
(5m)² = (3m)² +(2m+2)²
25m² = 9m² +4m² +8m +4
3m² -2m -1 = 0 . . . . . . . . . . . write in standard form, divide by 4
(m -1)(3m +1) = 0 . . . . . . . . factor
The positive solution for m is the value that makes m-1=0. It is m=1.
The side lengths are ...
5m = 5 . . . hypotenuse
3m = 3
2m+2 = 4
__
<u>2m+2 is the hypotenuse</u>
(2m+2)² = (5m)² +(3m)²
15m² -4m -2 = 0 . . . . . . . write in standard form, divide by 2
Then the solutions using the quadratic formula are ...
m = (-(-4) ± √((-4)² -4(15)(-2)))/(2(15)) = (4 ± √136)/30 = (2±√34)/15
The positive solution for m is ...
m = (2+√34)/15 ≈ 0.522063
Then the side lengths of the triangle are ...
(2m +2) = (34 +2√34)/15 ≈ 3.0441 . . . hypotenuse
5m = (2 +√34)/3 ≈ 2.6103
3m = (2 +√34)/5 ≈ 1.5662
