Answer:
width = 11
lenght = 13
Step-by-step explanation:
The area (A) of a tringle is:
A = wl
where
A = area
w = width
l = lenght
In this exercise, we know that:
A = 143 feet²
w = x
l = x + 2
We can substitute this values in the general formula and find the value of x:
A = wl
143 = (x)(x + 2)
143 = x² + 2x
x² + 2x - 143 = 0
Now we have a quadratic equation and we can solve it using the Quadratic formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{\Delta}}{2a}\text{ ; }\Delta=b^2-4ac \\ In\text{ this exercise:} \\ \Delta=2^2-4\cdot1\cdot(-143) \\ \Delta=4+572 \\ \Delta=576 \\ x=\frac{-2\pm\sqrt[]{576}}{2\cdot1} \\ x=\frac{-2\pm24}{2} \\ x=\frac{22}{2}=11 \\ or \\ x=-\frac{26}{2}=-13 \end{gathered}[/tex]Since we can not have a negative value for x, x = 11
w = 11
l = 13
