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.




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
Well area of a rectangle is given by the equation
a = L x W
Since they give us the expression for length and width we can find the expression for the area...
a = (3x - 4) x (2x - 5) or simply
a = (3x -4)(2x - 5)
Now we multiply
6x^2 - 15x - 8x + 20 =
6x^2 - 23x + 20
Your answer is C.