Find the length of the shorter leg...

Question

Find the length of the shorter leg of a right triangle if the longer leg is 4 feet more than the shorter leg and the hypotenuse is 4 feet less than twice the shorter leg.

Answer 1

x = length of shorter leg            (a)

x+4 = length of longer leg          (b) 

2x-4 = length of the hypotenuse  (c)

a² + b² =c²

(x)² +(x+4)² =(2x-4)²

 

x² +x² +8x+16 = 4x² -16x+16

2x² -24x = 0 

x(x-12)=0   

x = 0  or x=12

the length of a side of a triangle can not equal 0, so x=12

12 is the length of the shorter leg

 

check

12² +16² =20²

144+256=400

400=400 true

 

12 is the length of the shortest leg