Answer:
15 feet
Explanation:
Let's go ahead and draw a sketch as seen below;
We can go ahead and solve for x using the Pythagorean theorem as seen below;
[tex]\begin{gathered} 25^2=x^2+(x-5)^2 \\ 625=x^2+x^2-10x+25 \\ 625=2x^2-10x+25 \\ 2x^2-10x+25-625=0 \\ 2x^2-10x-600=0 \end{gathered}[/tex]Recall that a quadratic equation in standard form is given as;
[tex]ax^2+bx+c=0[/tex]Comparing both equations, we can see that a = 2, b = -10, and c = -600
We'll go ahead and use the quadratic formula to solve for x as seen below;
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt{(-10)^2-4(2)(-600)}}{2(2)} \\ x=\frac{10\pm\sqrt{4900}}{4} \\ x=\frac{10+\sqrt{4900}}{4},\frac{10-\sqrt{4900}}{4} \end{gathered}[/tex][tex]\begin{gathered} x=20,-15 \\ \therefore x=20\text{ or }x=-15 \end{gathered}[/tex]Since we're solving for distance, we'll go with the positive value of x which is 20. So x = 20 ft.
So the distance between the base of the ladder and the wall will be 15 ft (x - 5 = 20 - 5 = 15)
