SOLUTION:
Step 1 :
Set up the right triangle with the following:
side a = x
side b = 13 + 3x
side c = 14 + 3x
Using pythagorean theorem :
[tex]a^2+b^2=c^2[/tex]
[tex]x^2+(13+3x)^2=(14+3x)^2[/tex]
Step 2 :
Expand this equation by using foil to get:
[tex]x^2+(169+78x+9x^2)=196+84x+9x^2[/tex]
Simplifying this equation will give you:
[tex]x^2\text{ - 6 x - 27 = 0}[/tex]
Step 3 :
Factor this to get:
(x-9)(x +3) = 0
Solving this will give you x = 9 or x = -3.
The side length cannot be negative so discard the -3.
Step 4 :
Your side lengths will be:
[tex]\begin{gathered} a\text{ = x = 9 m} \\ b\text{ = 13 + 3 x = 13 + 3 ( 9 ) = 13 + 27 = 40 m} \\ \text{c = 14 + 3 x = 14 + 3 ( 9 ) = 14 + 27 = 41 m} \end{gathered}[/tex]
CONCLUSION:
The side lengths of the triangle are:
9 m , 40 m and 41 m
