The equations used to find the length of leg of triangle are:
[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]
Solution:
From given,
Area of right triangle = 24 square feet
Also from given figure in question (attached below )
base = x and height = x + 2
The area of triangle is given by formula:
[tex]Area = \frac{1}{2} \times base \times height[/tex]
Substituting the values we get,
[tex]24 = \frac{1}{2} \times x \times (x+2)\\\\24 = 0.5x(x + 2)\\\\48 = x(x+2)\\\\x^2 + 2x - 48 = 0\\\\[/tex]
Also, the above equation can be written as,
[tex]x^2 + (x+2)^2 =100[/tex]
Thus the equations used to find the length of leg of triangle are:
[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]
