Question

find the lengths of the missing sides. show your work.

8.
\\(h^2 = 3^2 + 2^2\\)
\\(h^2 = 9 + 4\\)
\\(h^2 = 13\\)
\\(h \approx 3.61\\)

9.
\\(h^2 = 5^2 + 4^2\\)
\\(h^2 = 25 + 16\\)
\\(h^2 = 41\\)
\\(h \approx 6.4\\)

10.
\\(h^2 = 6^2 + 20^2\\)

11.

12.
it is an isosceles triangle.

Explanation:

Solve Question 10

Using the Pythagorean Theorem knowledge point

$$
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$$

Solve Question 11

Using the Pythagorean Theorem knowledge point

$$
LATEXBLOCK1
$$

Solve Question 12

Using the Isosceles Right Triangle and Pythagorean Theorem knowledge points

$$
LATEXBLOCK2
$$

Estimate Square Roots

We can approximate non-perfect square roots by finding the nearest perfect squares.
For example, to estimate \(\sqrt{41}\):

• The nearest perfect squares are \(36\) and \(49\).
• Since \(36 < 41 < 49\), we know \(6 < \sqrt{41} < 7\).
• Because \(41\) is slightly closer to \(36\) than to \(49\), \(\sqrt{41} \approx 6.4\).

Answer:

Question 10

\(h \approx 20.9\) (or \(\sqrt{436}\))

Question 11

\(h \approx 9.4\) (or \(\sqrt{89}\))

Question 12

\(h \approx 12.7\) (or \(\sqrt{162}\))