CPM Homework Help : INT3 Problem 8-82

After finding out that her kitchen does not conform to industry standards, Lashayia is back to the drawing board (see problem 8-70). Where can she locate her sink along her counter in the top of the diagram at right so that its distance from the stove and refrigerator is as small as possible? Will this location make her perimeter less than $26$ feet? Show all work.

Hint:

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

Step 1:

Set up a proportion 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 $x$ .

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.