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6-8 Accelerated 7 Unit 8 Lesson 6

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IM K-5 Math
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Unit 8, Lesson 6

Finding Side Lengths of Triangles

Accelerated 7

Practice

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.

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Lesson 6 Resources

Student Materials

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 \(z\).

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

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Problem 3

The lengths of the three sides (in units) 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, \(\sqrt{2}, \sqrt7\)

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Problem 4

from an earlier course

Order the following expressions from least to greatest.

\(25\div 10\)

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

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

\(0.025\div 1\)

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Problem 5

ForLesson 4: Rational and Irrational Numbers

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

\(\text- \sqrt{10}\) is irrational because it is a square root.
\(\text- \sqrt{10}\) 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 it cannot be written as a positive or negative fraction.

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Problem 6

ForLesson 13: Adding and Subtracting with Scientific Notation

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?

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