# Lesson 10

Rectangles and Triangles with Fractional Lengths

### Problem 1

1. Find the unknown side length of the rectangle if its area is 11 m2. Show your reasoning.
2. Check your answer by multiplying it by the given side length ($$3\frac 23$$). Is the resulting product 11? If not, revise your previous work.

### Problem 2

A worker is tiling the floor of a rectangular room that is 12 feet by 15 feet. The tiles are square with side lengths $$1\frac13$$ feet. How many tiles are needed to cover the entire floor? Show your reasoning.

### Problem 3

The area of a rectangle is $$17\frac12$$ in2 and its shorter side is $$3\frac12$$ in. Draw a diagram that shows this information. What is the length of the longer side?

### Problem 4

The triangle has an area of $$7\frac{7}{8}$$ cm2 and a base of $$5\frac14$$ cm.

What is the length of $$h$$? Explain your reasoning.

### Problem 5

Find the value of $$\frac{5}{32}\div \frac{25}{4}$$. Show your reasoning.

### Solution

A builder is building a fence with $$6\frac14$$-inch-wide wooden boards, arranged side-by-side with no gaps or overlaps. How many boards are needed to build a fence that is 150 inches long? Show your reasoning.