hypotenuse is 8 inches longer that the shorter leg. The longer leg is 4 inches longer than the shorter leg. Find the length of the shorter leg.

Question

I can't understand how to put the words into an equation to solve it.

Answer 1

let a be the shorter leg, let b be the longer leg, and let c be the hypotenuse

 

So the statement of the problem says the following:

 

c = a + 8

b = a + 4

 

But there's one more thing that you know:  a² + b² = c²

 

So plug in those two expressions for c and b

 

a² + (a+4)² = (a+8)²

 

So...

 

a² + a² + 8a + 16 = a² + 16a + 64

2a² + 8a + 16 = a² + 16a + 64

 

Subtract a² from both sides:

a² + 8a + 16 = 16a + 64

 

Subtract 16a from both sides:

a² - 8a + 16 = 64

 

Subtract 64 from both sides:

a² - 8a + 48 = 0

 

Solve this equation.  You can do it by factoring:

(a-12)(a+4) = 0

 

So a = 12 or -4.

 

But -4 doesn't make sense because the length of a side can't be negative.  So the answer is that a = 12, which is the length of the shorter leg.