Answer:
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
