### Home > INT3 > Chapter 8 > Lesson 8.2.2 > Problem8-82

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. Homework Help ✎

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

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

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

Solve for $x$.