The longer leg of a right triangle is 1cm longer than the shorter leg.

Question

The longer leg of a right triangle is
1cm
longer than the shorter leg. The hypotenuse is
9cm
longer than the shorter leg. Find the side lengths of the triangle.

 

shortest leg=

longest leg=

hypotenuse=

Answer 1

n=shorter leg

n+1=longer leg

n+9=hypotenuse

n²+(n+1)²=(n+9)²

n²+n²+2n+1=n²+18n+81

2n²+2n+1-n²-18n-81=0

n²-16n-80=0

(n-20)(n+4)=0

n-20=0

n=20 cm (shorter leg)

n+1=21 cm (longer leg)

n+9=29 cm (hypotenuse)

Answer 2

Hi Kay,

 

Let x = shortest leg

Let x+1 = longer leg

let x + 9 = Hypotenuse

 

so then

 

x² + (x + 1)² = (x + 9)²

 

x² + x² +2x + 1 = x² + 18x + 81

 

x² -16x -80 = 0

 

(x -20)(x+4) = 0

 

x-20=0

 

x = 20  (this is the only factor that works since the other one is negative

 

therefore

 

x = 20

x+1 = 21

x+9 = 29

 

Hope this helps