theorem number 5

Question

Use the Pythagorean theorem to find the missing side.



c=11?,

b=6a;
find a and b

Answer 1

The pythagorean theorem is as follows:

 

a²+b²=c²

 

Where c is the hypotenuse and a and b are the side lengths. Let's plug in what we know;

 

a²+(6a)²=(11)²

 

As you can see, we have one equation with one unknown (a), so we can solve this equation for a. 

 

a²+(6²*a²) = (11)²

 

a²+36*(a²) = 121

 

37(a²) =121

 

a² = 121/37

 

Take the square root of 121/37 and we will have a. **Note, normally, we would want to take the positive and negative square root when solving this equation. However, since this involves side lengths of a triangle, and we cannot have a negative measurement, we will only use the positive value. 

 

To find b, we use the equation

 

b = 6a

 

Simply plug in what we get for a and this will give us b.