Are there primitive triples that cannot be obtained through this method? Class 8

Are there primitive triples that cannot be obtained through this method? Class 8

Question 1.

Are there primitive triples that cannot be obtained through this method? Class 8

If yes, give examples.

Solution:

Yes. For example, (8, 15, 17), (12, 35, 37).

Question 2.

Find the diagonal of a square with sidelength 5 cm. Class 8

Solution:

Diagonal = [latex]\sqrt{5^2+5^2}[/latex] = [latex]5 \sqrt{2}[/latex] cm.

Question 3.

Find the missing sidelengths in the following right triangles : Class 8

Solution:

7² + 9² = 49 + 81 = 130.

So, sidelength = [latex]\sqrt{130}[/latex].

4² + 10² = 116. So, length = [latex]\sqrt{116}[/latex] = [latex]2 \sqrt{29}[/latex].

41² - 40² = (41 + 40) (41 - 40) = 81 × 1 = 81.

So, length = [latex]\sqrt{81}[/latex] = 9.

[latex]\sqrt{200^2}[/latex] - 10² = 200 - 100 = 100.

So, sidelength = [latex]\sqrt{100}[/latex] = 10.

10² + [latex]\sqrt{150^2}[/latex] = 100 + 150 = 250.

So, sidelength = [latex]\sqrt{250}[/latex] = [latex]5 \sqrt{10}[/latex].

45² - 27² = (45 + 27) (45 - 27) = 72 × 18.

So, sidelength = [latex]\sqrt{72 \times 18}[/latex] = 36.