Two students while solving a quadratic equation in x one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coeffficient of x² as -6 and 1 respectively. The correct roots are

8 miles and 4 miles

Step-by-step explanation:

Area of a triangle = 1/2 bh = 16 square miles

From the question, one of the legs is 4 miles greater than the other leg

Let's pick b; the breadth as the longer leg and h; the height as the shorter leg

So, b = 4 + h

Now, we'll slot in the values of b and h

This gives;

1/2 ( 4 + h ) * h = 16

Cross multiply

( 4+ h ) * h = 2(16)

4h + h^2 = 32

Let's equate the equation to zero to form a quadratic equation

4h + h^2 - 32 = 0

Rearrange

h^2 + 4h - 32 = 0

Two numbers that when they are multiplied give - 32 and when they are summed up give +4 are +8 and -4

Slot in these numbers in the equation

h^2 + 8h - 4h - 32 = 0

h( h + 8 ) -4 ( h + 8 ) = 0

( h + 8 ) ( h - 4 ) = 0

h + 8 = 0                       h - 4 = 0

h = -8                            h = 4

Taking the positive value of h, we have that h = 4 miles

Now let's substitute the value of h in b = 4 + h

b = 4 + 4

b = 8 miles

Check

16 = 1/2 *8*4

16 = 1/2 * 32

16 = 16

Therefore, the length of the longer side is 8 miles and that of the shorter side is 4 miles