CPM Homework Help : GC Problem 7-97

After finding out that her kitchen does not conform to industry standards, Lashayia is back to the drawing board (see problem 7-73). Where can she locate her sink along her top counter so that its distance from the stove and refrigerator is as small as possible? And will this location keep her perimeter below $26$ feet? Show all work.

A diagram of a u shaped kitchen counter, showing the perimeter of a triangle, connecting the center of Refrigerator F, at end of left counter, to the center of stove, at end of right counter, & to an unidentified point on the back counter, distances labeled, back counter is 11 feet, left counter is 6 feet, right counter is 3 feet.

Hint:

This problem is similar to the Interior Design problem from Lesson 7.1.3. How did you find the solution for that problem?

More Help:

For the shortest possible distance, the two right triangles should be similar.

Next Step:

Set up equivalent ratios of corresponding sides: Remember the side that is length $11$ , can be split into two lengths $x$ and $11−x$ .

$\frac{6}{x}= \frac{3}{11-x}$

Step 2:

Solve for $x$ .