Find the length of missing leg

Question

One leg of a right triangle is 4cm shorter than the other leg . The length of the hypotenuse is 20cm find the length of the shorter leg

Answer 1

20² = x² + (x-4)²

 

Solve!

 

Or guess that it's a 20-16-12 right triangle (four times the ubiquitous 5-4-3 rt. triangle).

Answer 2

Let x be the length of the shorter leg.  then the longer leg is x+4.  Now use the Pythagorean Theorem.

 

c² = a² + b²

20² = x² + (x + 4)²

400 = x² + x² + 8x + 16

400 = 2x² + 8x + 16

2x² + 8x - 384 = 0

2(x² + 4x - 192) = 0

2(x + 16)(x - 12) = 0

x + 16 = 0     x = -16

x - 12 = 0     x = 12

 

The shorter leg is x, and it can't be a negative number, so it is 12 cm.