The figure shows a right triangle. Find the length of the shortest side of the triangle.

Pls Refer to the image below.

x= 18cm

Step-by-step explanation:

Applying pythagoras' rule

(x)²+(x+6)²=(x+12)²

Open the brackets

x²+x²+12x+36=x²+24x+144

Collect like terms to the LHS

x²+x²-x²+12x-24x+36-144=0

x²-12x-108=0

Solving the quadratic equation

a=1,b= - 24,c= - 108,ac= - 108

Factors are - 18 & +6

x²-18x+6x-108=0

(x²-18x)+(6x-108)=0

x(x-18)+6(x-18)=0

(x-18)(x+6)=0

x-18=0 or x+6=0

x=0+18 or x=0-6

x=18 or x= - 6

In cases like this it's the positive answers that are chosen

Therefore, x=18cm