To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{64} \) = 8

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 8² + 8²
c² = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

c² - 15c + 56 = 0
(c - 7)(c - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 7) or (c - 8) must equal zero:

If (c - 7) = 0, c must equal 7
If (c - 8) = 0, c must equal 8

So the solution is that c = 7 or 8

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

-3b + 7y = 9b - 3y + 9
-3b = 9b - 3y + 9 - 7y
-3b - 9b = -3y + 9 - 7y
-12b = -10y + 9
b = \( \frac{-10y + 9}{-12} \)
b = \( \frac{-10y}{-12} \) + \( \frac{9}{-12} \)
b = \(\frac{5}{6}\)y - \(\frac{3}{4}\)