The shorter leg of a right triangle is 5 meters. The hypotenuse is 1 meter longer than the longer leg. Find the length of the longer leg.

Question

pythagorean theorem

Answer 1

a² + b² = c²

 

Here's what we know:

b = 5

c = a + 1

 

So:

a² + 5² = (a+1)(a+1)

a² + 25 = a² + 2a +1

25 = 2a + 1

24 = 2a

12 = a

 

This also means the hypotenuse is 13 meters

 

Let's check our answer:

12² + 5² = 13²

144 + 25 = 169

169 = 169

 

So the longer leg is 12 meters long.