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 = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

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 = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 8 + 9 + 6 + 3
p = 26

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

y² + 2y - 4 = 4y - 1
y² + 2y - 4 + 1 = 4y
y² + 2y - 4y - 3 = 0
y² - 2y - 3 = 0

Next, factor the quadratic equation:

y² - 2y - 3 = 0
(y + 1)(y - 3) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 1) or (y - 3) must equal zero:

If (y + 1) = 0, y must equal -1
If (y - 3) = 0, y must equal 3

So the solution is that y = -1 or 3

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(8a)(5ab) + (5a²)(3b)
(8 x 5)(a x a x b) + (5 x 3)(a² x b)
(40)(a¹⁺¹ x b) + (15)(a²b)
40a²b + 15a²b
55a²b

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

6a² + 5a² = 11a²