Solving problem on Pythagorean Theorem

Solving Problem Pythagorean Theorem


2 2
a + b =c
2
Pythagorean Theorem formula
Where, a represents for a shorter leg
b represents for a longer leg
c represents the hypotenuse
Example:
1. The three sides of right triangle are x + 1, x + 2, and x+3. What are the measures of the shorter leg, longer
leg, and hypotenuse?


x +1 x+3


x+2
Solutions:
2 2 2
a + b =c
2 2 2
( x +1) +(x+ 2) =(x+ 3)

(x +1)( x +1)+ ( x+ 2 )( x +2 )=( x+ 3)( x +3) Apply the FOIL Method.
( x 2 + 2x + 1) + ( x 2+ 4 x +4 ) = ( x 2+ 6 x+ 9)
2 x 2 + 6x + 5 = x 2+ 6 x+ 9
2 x 2−x 2+ 6 x−6 x+5−9=0
x −4 = 0
2



x=4 Square both sides.
2



x=2
Shorter leg = (x+1) Longer leg = (x+2) Hypotenuse = (x+3)
= (2+1) = (2+2) = (2+3)
Shorter leg = 3 Longer leg = 4 Hypotenuse = 5
Exercise:
1. The three sides of right triangle are x + 1, x + 8, and x + 9. What are the measures of the shorter leg, longer
leg, and hypotenuse?
x
x+9
x+1


x+8