# Lesson 5

Finding Side Lengths of Triangles

Let’s find triangle side lengths.

### Problem 1

Here is a diagram of an acute triangle and three squares.

Priya says the area of the large unmarked square is 26 square units because \(9+17=26\). Do you agree? Explain your reasoning.

### Problem 2

\(m\), \(p\), and \(z\) represent the lengths of the three sides of this right triangle.

Select **all** the equations that represent the relationship between \(m\), \(p\), and \(z\).

\(m^2+p^2=z^2\)

\(m^2=p^2+z^2\)

\(m^2=z^2+p^2\)

\(p^2+m^2=z^2\)

\(z^2+p^2=m^2\)

\(p^2+z^2=m^2\)

### Problem 3

The lengths of the three sides are given for several right triangles. For each, write an equation that expresses the relationship between the lengths of the three sides.

- 10, 6, 8
- \(\sqrt5, \sqrt3, \sqrt8\)
- 5, \(\sqrt5, \sqrt{30}\)
- 1, \(\sqrt{37}\), 6
- 3, \(\sqrt{2}, \sqrt7\)

### Problem 4

A one-quart container of tomato soup is shaped like a rectangular prism. A soup bowl shaped like a hemisphere can hold 8 oz of liquid. How many bowls will the soup container fill? Recall that 1 quart is equivalent to 32 fluid ounces (oz).

### Problem 5

Which is the best explanation for why \(\text-\sqrt{10}\) is irrational?

\(\text- \sqrt{10}\) is irrational because it is not rational.

\(\text- \sqrt{10}\) is irrational because it is less than zero.

\(\text- \sqrt{10}\) is irrational because it is not a whole number.

\(\text- \sqrt{10}\) is irrational because if I put \(\text- \sqrt{10}\) into a calculator, I get -3.16227766, which does not make a repeating pattern.

### Problem 6

A teacher tells her students she is just over 1 and \(\frac{1}{2}\) billion seconds old.

- Write her age in seconds using scientific notation.
- What is a more reasonable unit of measurement for this situation?
- How old is she when you use a more reasonable unit of measurement?