Lesson 6: Practice Problems

Problem 1

  1. Find the lengths of the unlabeled sides.

    A right triangle with a horizontal side on the top and a vertical side on the left. The top side is labeled 6 and the side on the left is labeled 2.
    A right triangle with a horizontal side on top and a vertical side on the left. The top side is labeled 8 and the left side is labeled 6.

  2. One segment is units long and the other is units long. Find the value of and . (Each small grid square is 1 square unit.)

    A line segment labeled “n” on a square grid. The line segment starts at an intersection point on the grid and slants downward and to the right to an end point that is 1 unit to the right and 3 units down.
    A line segment labeled “p” on a square grid. The line segment starts at an intersection point on the grid and slants upward and to the right to an end point that is 3 units to the right and 4 units up.

Problem 2

Use the areas of the two identical squares to explain why without doing any calculations.

Squares of side lengths 5 and 12. Figure 1 has internal lines drawn making a 5 x 5 square. Figure 2 has an inscribed square with side lengths of 13.

Problem 3

Find the exact value of each variable that represents a side length in a right triangle.

  1. A right triangle with legs 8 and h and hypotenuse 10.
  2. A right triangle with legs 6 and k and hypotenuse 6.5.
  3. A right triangle with legs 2 and m and hypotenuse 5.
  4. A right triangle with legs square root of 10 and n and hypotenuse 10.
  5. A right triangle with legs square root of 68 and p and hypotenuse square root of 85.

Problem 4 From Unit 7 Lesson 4

Write each expression as a single power of 10.

Problem 5 From Unit 5 Lesson 21

Here is a scatter plot of weight vs. age for different Dobermans. The model, represented by , is graphed with the scatter plot. Here, represents age in weeks, and represents weight in pounds.

A scatter plot of age (weeks) (horizontal from 0-25) and weight (pounds) (vertical from 0 to 80), with a line of best fit sloping upwards.

  1. What does the slope mean in this situation?

  2. Based on this model, how heavy would you expect a newborn Doberman to be?