Find the lengths of the legs

Question

A right triangle has one leg that is 3 inches longer than the other leg. The hypotenuse is the square root of 65 inches.

Answer 1

Hey Jessica,

 

To solve this problem, we need to use what we know about the sides of right triangles. We know that c²=a²+b²

In this case, a=a and b=a+3 and c=√64. The equation will then look something like this:

 

(√64)²=a²+(a+3)²

 

This simplifies to

 

64=a²+(a²+6a+9)

64=2a²+6a+9

 

Now, to solve for a, we'll need to use the dreaded quadratic formula. To get the equation into that format, we'll subtract 64 from both sides and factor out the 2. That gives us:

 

0=a²+3a-28

Plugging that in the quadratic formula will look like this:

 

(-3+/- √(3²-(4)(1)(-28)))/2

 

(-3+/- √9+112)/2

 

(-3+/-√121)/2

(-3+/-11)/2

8/2 or -14/2

 

that gives us a=4 or -7. Since the length can't be negative, we know a=4 and b=4+3=7

 

Hope that helps,

Nikita