The area of a right triangle is 16 square miles. One leg of the triangle is 4 miles longer than the other leg. Find the length of each leg

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

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: