Question

A 25ft ladder is standing up against a wall . The distance between the base of the ladder and the wall is 5ft less than the distance between the top of the ladder snd the base of wall . Find the distance between the base base of the ladder and the wall

Answer 1

15 feet

Step-by-step 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;

`\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}`

Recall that a quadratic equation in standard form is given as;

`ax^2+bx+c=0`

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;

`x=(-b\pm√(b^2-4ac))/(2a)`
`\begin{gathered} x=(-(-10)\pm√((-10)^2-4(2)(-600)))/(2(2)) \\ x=(10\pm√(4900))/(4) \\ x=(10+√(4900))/(4),(10-√(4900))/(4) \end{gathered}`
`\begin{gathered} x=20,-15 \\ \therefore x=20\text{ or }x=-15 \end{gathered}`

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)