Lesson 6

Finding Side Lengths of Triangles

Problem 1

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

An acute triangle with squares along each side of the triangle.

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

 

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 2

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

Right triangle, legs = p, z, hypotenuse = m

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

A:

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

B:

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

C:

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

D:

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

E:

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

F:

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

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

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.

  1. 10, 6, 8
  2. \(\sqrt5, \sqrt3, \sqrt8\)
  3. 5, \(\sqrt5, \sqrt{30}\)
  4. 1, \(\sqrt{37}\), 6
  5. 3, \(\sqrt{2}, \sqrt7\)

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 4

Order the following expressions from least to greatest.

\(25\div 10\)

\(250,\!000 \div 1,\!000\)

\(2.5 \div 1,\!000\)

\(0.025\div 1\)

 

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 4, Lesson 1.)

Problem 5

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

A:

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

B:

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

C:

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

D:

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

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 8, Lesson 3.)

Problem 6

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

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

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 7, Lesson 15.)