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chrysanthemum
Hello!

6.
Since the area is that of a square, you know that all side lengths are the same. 

Area is base times height (A = bh), but since base and height are the same for a square, you get the formula A = a².

[tex]A = a^{2} [/tex]
[tex]144 = a^{2} [/tex]
[tex] \sqrt{144} = a[/tex]
[tex]12 = a[/tex]

The length of the side of a square with an area of 144 in² is 12 in.

7.
Rational number.

8.
This is a right triangle; use the Pythagorean Theorem to find missing lengths of right triangles. Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.

Plug in your leg lengths:

a² + b² = c²
8² + x² = 21²
64 + x² = 441
x² = 377
x = 19.4