Find the lengths of the legs

The hypotenuse of a right triangle is 16 ft long.  One leg is 6.6 ft longer than the other leg.  Find the lengths of the legs.  Round to one decimal place.

x = one leg
x + 6.6 = other leg

The Pythagorean Theorem is a² + b² = c² , where a and b are the legs and c is the hypotenuse (the side across
from the right angle}  The Pythagorean Theorem states that the sum of the squares of the legs is equal to the
square of the hypotenuse.

So, here we go.
a² + b² = c²   {the Pythagorean Theorem}
x² + (x + 6.6)² = 16²    {substituted the sides into the Pythagorean Theorem}
x² + x² + 13.2x + 43.56 = 256   {squared the binomial, (x + 6.6) and squared the 16}
2x² + 13.2x - 212.44 = 0  {combined like terms and subtracted 256 from each side}

To solve the quadratic equation for x, graph the equation on the graphing calculator, to identify where the
graph hits the x-axis.  That is the value of x.

So, you see in the graph that the x-intercept is
approximately  -14.1 and 7.5.  However, the leg of a triangle cannot be negative.  Therefore, x ≈ 7.522

one leg is 7.5 ft   {rounded to the nearest tenth}
the other leg is 14.1  
{substituted 7.522, in for x, into (x + 6.6)
​and rounded to the nearest tenth}

Putting those back into the Pythagorean Theorem:
a² + b² = c² 
(7.522)² + (14.122)² ≈ 16² 
56.58 + 199.43  ≈ 256
256.01 ≈ 256  and it worked!

Note:  the more decimal places you keep in your
work as you are working through the problem, the
more accurate your answer will be.

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