Chapter 9.8, Problem 12P

To determine

To calculate:

The value of the distance for shorter ladder and longer ladder from building

Answer to Problem 12P

The value of the distance for shorter ladder and longer ladder from building is

Explanation of Solution

Given information:

Shorter ladder: $20m$

Longer ladder: $15m$

Calculation:

Consider,

The distance: $d$

The equations are formed as:

Here, two right triangles are with the same height $h$ for one of the legs and the other legs are $d$ and $7+d$ , and the two hypotenuses are $15$ and $20$ respectively. Using the Pythagorean Theorem:

  ${20}^2=h^2+{\left(d+7\right)}^2$  ... (1)

  ${15}^2=h^2+d^2$  ... (2)

Expanding eq. (1):

  $400=h^2+d^2+14d+49$

From eq. (2):

  $\begin{array}{l}400={15}^2+14d+49\\ 14d=426\\ d=9\end{array}$

The shorter ladder is $9m$ from the building and the longer ladder is $7+d=7+9=16m$ from the building.